Write log3 6 as a logarithm of base 2

a. log base 2 of 3 over log base 2 of 6

b. log base 2 of 6 over log base 2 of 3

c. log base 3 of 2 over log base 6 of 2

d. log base 6 of 2 over log base 3 of 2

Answers

Answer 1
you should end with B as the correct answer  but be careful not to mix it up with D 
Answer 2

Final answer:

The expression log3 6 can be converted to a logarithm of base 2 using the change of base formula, which results in log2 6 / log2 3. So the correct option is b.

Explanation:

The student asked how to express log3 6 as a logarithm with a base of 2. To perform this conversion, we can use the change of base formula, which states that logab = logcb / logca for any positive numbers a, b, and c, where a and c are not equal to 1. In this formula, 'c' can be any base, but in our case, we will use base 2 since that's what the question requires.

So, by applying the change of base formula, we can write:

log₃6 = log₂6 / log₂3

Therefore, the correct option that represents log3 6 as a logarithm of base 2 is:

(b) log₂6 / log₂3

Related Questions

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h
A=H(A+B)/2
Solve for b.
A. B=Ah/2-a
B. B=2A/h+a
C. B=2A/h-a
D. B=2A-a/h

Answers

Given that the formula for a trapezoid that relates the area A, the two bases, a and b, and the height, h is given by:

[tex]A= \frac{h(a+b)}{2} [/tex]

To solve for b, first multiply both sides by 2 to get:

2A = h(a + b) = ah + bh

Next, subtract ah from both sides to get:

2A - ah = bh

Next, divide both sides by h, to get:

[tex] \frac{(2A-ah)}{h} =b \\ \\ \therefore b=\frac{2A-ah}{h}[/tex]

Answer:

The answer is b=2A/h-a

Ellen walks dogs on weekends. She gets paid $8.50 per hour. Each day she works five hours and 45 minutes. How much does Ellen get paid per weekend?

Answers

48.875 i believe is the answer hope it helps!!!

Amy is eight years older than twice her cousin Alicia’s age. The sum of their ages is less than 32. Let x represent Alicia's age. Which inequality represents Alicia’s possible age? 0
0
0

0

Answers

Assume that the age of Alicia is x and that of Amy is y
Twice the age of Alicia = 27
Eight years older means we will add 8
Therefore, the statement "Amy is eight years older than twice her cousin Alicia’s age" can be represented as follows:
y = 8 + 2x (equation)
The sum of their ages is less than 32 can be represented as:
x + y < 32 which can also be written as y < 32-x (inequality)

Oliver is working on a puzzle of the Eiffel Tower. The tower in the puzzle is 28.5 in. tall. The packaging lists the scale as 1:415. What is the height of the actual Eiffel tower to the nearest foot?

Answers

In the puzzle 1 is equivalent to 415 in reality.

If you have 28.5 in tall, you need to multiply by 415

( 28.5 in ) ( 415 ) = 11827.5 in 

The heigh of the actual eiffel tower is: 11827.5 in

1 foot = 12 in.

11827.5 in / 12 in = 985.625 ft   

The heigh of the actual eiffel tower is: 986 ft


can someone help me out

Answers

I don't see in the problem what she is paid for over time but it is normally 1.5 times per hour

 so 40 hours at 25 = 1000

51-40 = 11 hours of over time

25 *1.5 = 37.50 per hour for over time

11 * 37.50 = 412.50

1000+412.50 = 1412.50 total

Plz help! Convert 3/5 into fractions with a denominater of 15 A.9/15 B. 3/15 C.5/15 D. 6/15

Answers

Because we need to multiply the bottom by 3 to get 15, we need to multiply the top as well:

3*3/5*3
9/15

Hope this helped!

What is the slope of the line shown?

Answers

the slope is positive 9/7 bc you go up 9 from the first point and 7 to the right

Answer:

Option (b) is correct.

The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]

Step-by-step explanation:

Given: A graph with an equation of line having two points (1,6) and  (-6, -3)

We have to find the slope of the given line in graph and choose the correct from the given options.

Consider the two points (1,6) and  (-6, -3).

Slope between two points can be calculated using the formula as,

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex]\left(x_1,\:y_1\right)=\left(1,\:6\right),\:\left(x_2,\:y_2\right)=\left(-6,\:-3\right)[/tex]

Thus, Slope is

[tex]m=\frac{-3-6}{-6-1}=\frac{9}{7}[/tex]

Thus, The slope of line shown in given graph is [tex]\frac{9}{7}[/tex]

Line SV is an angle bisector of angle RST if angle RSV = (3x+5) and angle RST = (8x-14) find x

Answers

SV splits RST into 2 equal sections.

so RST = 2 * RSV

8x - 14 = 2(3x + 5)
8x - 14 = 6x + 10
8x - 6x = 10 + 14
2x = 24
x = 24/2
x = 12 <===

Answer:

x=12

Step-by-step explanation:

Line SV is an angle bisector of angle RST

<RSV = <VST

Both angles are equal

m<RSV = (3x+5)

<RSV = <VST, so m<VST = (3x+5), m<RST= 8x-14

m<RST= m<RSV +m<VST

[tex]8x-14= 3x+5+3x+5[/tex]

Combine like terms and solve for x

[tex]8x-14= 6x+10[/tex]

Subtract 6x from both sides

[tex]2x-14=10[/tex]

Add 14 on both sides

[tex]2x=24[/tex]

Divide both sides by 2

x=12

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if: (a) The candies are all the same and the lunch boxes are all different? (b) The candies are all different and the lunch boxes are all the same? (c) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different? Please explain your work IN DETAIL. Thanks!

Answers

It would be impossible because u don't have 3
The answer to this question is:

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if: (a) The candies are all the same and the lunch boxes are all different? (b) The candies are all different and the lunch boxes are all the same? (c) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different? Please explain your work IN DETAIL. Thanks!?.

A).4^3 = 64 

B).(3+4-1)C3 = 6c3 = 20 

C).3c3 +3c2 + 3c1 = 7 

The last Question). 4!/2! ways = 4+24+12 = 40 ways 

Hoped This Helped Alialbaghdadi6
Your Welcome :) 

The perimeter p of a rectangle is related to the length l and width w through the equation p=2l+2w. determine the width in terms of the perimeter and length.

Answers

To find the equation for width in terms of length and perimeter, we need to solve for w in the equation for perimeter:
[tex]p=2l+2w[/tex]
[tex]p-2l=2w[/tex]
[tex]\frac{1}{2}p-l=w[/tex]

The volume of a rectangular box is 2160 in cubes. It is 10 in. wide and 18 in. long. What is the height of the box?

Answers

height=voulme/length and width 
2160/18*10=12
12=height

a group of 10 people ran an average of 2.7 miles in one week. if the first 4 people in the group averaged 3 miles, what did the last 6 people average

Answers

In this question, 10 people average running distance is 2.7miles. Then the sum of their running distance would be: 10 people * 2.7 miles/people= 27 miles.

The group then divided into 2, 4 people with 3 miles average and 6 people with unknown average. Since the people are same like the 10 people group, their total running distance would be the same. The calculation would be:

total distance = group1 * average1 + group2 * average2
27 miles= 4 people * 3 miles/people + 6 people* average2
6 people * average2 = 27 miles -12 miles = 15 miles
average2= 15 miles/6people= 2.5 miles/people

Suppose it took 12 riders a total of 11 days 21 hours to ride from St.joseph to Sacremento. If they all rode the same number of hours how many hours did each rider ride

Answers

285 hours because there is 264 hours in 11 days and then you just add the 21 to the 264 because they're asking how many hours did each rider ride individually, not all together.

6(r+3)-4=2r+10+4r how do you slove that

Answers

Simplify 2r + 10 + 4r to 6r + 10

Expand it

Simplify 6r + 18 - 4 to 6r + 14

Cancel 6r on both sides

Since 14 = 10 is false, there is NO solution for this equation so no answer.
6(r+3) - 4 = 6r + 10    (simplify)

6r + 18 - 4 = 6r + 10 (distribute 6 into all)

6r + 14 = 6r + 10 (simplify)

6r - 6r = 10 - 14 

0 = -4 (untrue)

cannot be solved sorry

Explain why the equation 6|x| + 25 = 15 has no solution. When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution. When one solves, they arrive at a step where |x| is equal to a fraction that may not be represented as an integer. Since | x| must be an integer, there is no solution. When one solves, they arrive at a step where x is equal to a negative number. Since x can never be negative inside of the absolute value bars, there is no solution. The statement is false. There is a solution.

Answers

Final answer:

The equation 6|x| + 25 = 15 has no solution because it implies that |x| equals a negative number after simplification, and absolute values cannot be negative.

Explanation:

The equation 6|x| + 25 = 15 has no solution because the absolute value of x, denoted by |x|, represents the distance of x from zero on the number line, and as such, it can never be negative. When we solve the given equation, we isolate the absolute value on one side which gives us 6|x| = -10 after subtracting 25 from both sides. Dividing by 6, we obtain |x| = -10/6, which is a negative number. However, since an absolute value cannot equal a negative number, this indicates that there is no valid solution to the equation.



What is the median of the data set?


30 52 68 65 69 61 68 75 85 78
Question 2 options:


61


65.1


68


69

Answers

Answer: The answer is 68

The above answer is incorrect.

Step-by-step explanation:

What is the difference of the polynomials?


Answers

Answer:

2x^3 + 2x

Step-by-step explanation:

subtract the 2 x^4's

x^3 +x^3 = 2x^3

x +x = 2x

answer is 2x^3 + 2x

The difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]

Given the polynomials:

[tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex],

We are required to find their difference which can be solved as follows:

[tex](x^4 + x^3 + x^2 + x ) - ( x^4 - x^3 + x^2 - x)[/tex]

First, open the bracket by multiplying every term you have in [tex]( x^4 - x^3 + x^2 - x)[/tex] by -1:

Thus:

[tex]x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x[/tex]

Group like terms together and add them together

[tex]x^4 - x^4 + x^3 + x^3 + x^2 - x^2 + x + x\\\\\mathbf{2x^3 + 2x}[/tex]

Thus, the difference between the polynomials, [tex]x^4 + x^3 + x^2 + x $ and $ x^4 - x^3 + x^2 - x[/tex] is expressed as: [tex]\mathbf{2x^3 + 2x}[/tex]

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−42v+33<8v+91 solve for v

Answers

−42v+33<8v+91
33 - 91 < 8v + 42v
      -58 < 50v
 -58/50 < v
-29/25  < v
or 
v > -29/25



The value of v is v > -1.16.

What are Linear Inequalities?

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given linear inequality is

−42v + 33 < 8v + 91

We have to take like terms on one side.

-42v and 8v are like terms and 33 and 91 are like terms.

Subtracting 8v from both sides,

−42v + 33 - 8v < 8v + 91 - 8v

-50v + 33 < 91

Subtracting 33 from both sides,

-50v + 33 - 33 < 91 - 33

-50v < 58

Dividing both sides by -50, the inequality sign changes.

v > -58 / 50

v > -1.16

Hence the solution for the inequality is v > -1.16.

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what's the answer to this equation?

Answers

x^2-2x+2 is the same as 1x^2-2x+2

1x^2-2x+2 = 0 is in the form ax^2+bx+c = 0 where
a = 1
b = -2
c = 2

Plug these a,b,c values into the discriminant formula below
D = b^2 - 4ac
D = (-2)^2 - 4*(1)*(2)
D = -4

The final answer is -4

Plzzzz Help mee with the there questions i dont like math :P

Answers

-6 on the first term...and on the next 3 turns..
-6 + 3(-6) = -6 - 18 = - 24 <==
=====================
declines 3 degrees every hr for 5 hrs..
5(-3) = -15 <==
=====================
200 - 18(8) = 200 - 144 = 56 <=

y+6x=11; x= -1, 0, 4

solve the equation for y then find the value of y for each value of x

Answers

y+6(-1)=11, y+(-6)=11, y=17

y+6(0)= 11, y= 11


y+6(4)= 11, y+24= 11, y= -13

That's all I got. Hope its helpful
minus 6x from both sides

y=-6x+11

ok, so when x=-1
y=-6(x)+11
y=-6(-1)+11
y=6+11
y=17
when x=-1, y=17

when x=0
y=-6(0)+11
y=-6(0)+11
y=0+11
y=11
when x=0, y=11

when x=4
y=-6(x)+11
y=-6(4)+11
y=-24+11
y=-13
when x=4, y=-13

if that is the wrong answer then what is the right answer .

Answers

well whats the question

is someone can help me please please i will give 20 points please

Answers

With an inverse function, we essentially solve for x and then switch f(x) (which can be called y) with x. For y=x/8-7, we add 7 to both sides to get y+7=x/8. Multiplying both sides by 8, we get 8*(y+7)=x. Switching y and x, we get 8*(x+7)=y. This is shown as the third option.

For y=20-0.25x, we can subtract 20 from both sides to get y-20=-0.25x. Next, we can multiply both sides by -1 to get 0.25x=-y+20=20-y. Multiplying both sides by 4 (since 1/4=0.25 and we want to find x), we get x=4(20-y). Switching x and y, we get y=4(20-x), which is the first option. I challenge you to do the other two based off of the techniques I used!

Of the ice cream cones sold yesterday at percy's ice cream shop, 1/3 were chocolate and another 1/2 were vanilla. what fraction of the ice cream cones sold were either chocolate or vanilla

Answers

Fraction of either vanilla or chocolate = 1/3 + 1/2 = 2/6 + 3/6 = 5/6

The required fraction of the ice cream cones sold were either chocolate or vanilla is 5/6.

What is  Least Common Denominator?

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

We have been given that of the ice cream cones sold yesterday at Percy's ice cream shop, 1/3 were chocolate and another 1/2 were vanilla.

We have to determine the fraction of the ice cream cones sold were either chocolate or vanilla

1/3 equals 2/6

According to the given question,

The fraction of either vanilla or chocolate will be:

⇒ 1/3 + 1/2

Change into a lowest common denominator,

⇒  2/6 + 3/6

Apply the addition operation to get

⇒  5/6

Therefore, the required fraction of either vanilla or chocolate is 5/6.

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Seven years ago, kodi found a box of old baseball cards in the garage. since then, he has added a consistent number of cards to the collection each year. he had 52 cards in the collection after 3 years and now has 108 cards. kodi looking into his box of baseball cards. how many cards were in the original box? is this t(0) or t(1)? write the first few terms of the sequence. kodi plans to keep the collection for a long time. how many cards will the collection contain 10 years from now? write an equation that determines the number of cards in the collection after n years. what does each number in your rule represent?

Answers

(3,52)(7,108)
slope = (108 - 52) / (7 - 3) = 56/4 = 14

y = mx + b
slope(m) = 14
(3,52)...x = 3 and y = 52
sub and find b, the y int (the original amount of cards)
52 = 3(14) + b
52 = 42 + b
52 - 42 = b
10 = b

so ur equation is y = 14x + 10....with x being the number of years and y being the total cards. <== ur equation is y = 14x + 10

He started with 10 cards....and has been adding 14 cards every year.

so after 10 years...
y = 14(10) + 10
y = 140 + 10
y = 150 <== after 10 years, he will have 150 cards

The required equation is y = 14x + 10 which is the number of cards in the collection and he will have 150 cards after 10 years

What is the slope of the line?

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

As per the question, we take the two points are (3,52) (7,108)

So slope = (108 - 52) / (7 - 3) = 56/4 = 14

y = mx + b

slope(m) = 14

Substitute the value of x = 3 and y = 52 in the equation

52 = 3(14) + b

52 = 42 + b

52 - 42 = b

10 = b

So the original amount of cards is 10

If x represents the number of years, while y is the total number of cards.

y = 14x + 10

He began with 10 cards and has added 14 cards every year thereafter.

So after 10 years

y = 14(10) + 10

y = 140 + 10

y = 150

Therefore, he will have 150 cards after 10 years

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What is the radius of a circle with circumference 27 in.?

Answers

Okay. So, the circumference equals pi * diameter. What we would have to do is divide 27 by pi (3.14). When you divide, you should get 8.598 and other numbers behind it or 8.6 when rounded to the nearest tenth. The radius is half of the diameter, so you do 8.6/2. When you do that, your quotient should be 4.3. The radius of a circle with a circumference of 27 in. is 4.3 in.
Final answer:

The radius of a circle with a circumference of 27 inches can be calculated using the formula for the circumference of a circle which is 2πr. Calculating this, the radius is approximately 4.3 inches.

Explanation:

The subject of this question is Mathematics, more specifically, Geometry which deals with shapes, sizes and properties of figures. In this case, we are being asked to find the radius of a circle given its circumference. The circumference of a circle is calculated as 2πr, where r represents the radius and π is approximately equal to 3.14.

To find the radius (r), you would divide the circumference by 2π. Given that the circumference of the circle is 27 inches, we divide 27 by 2π (approximately 6.28). This can be further simplified to approximately 4.3 inches.

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Evaluate cot675°. i will give brainlist

Answers

cot 675  = cot (675 - 360)  =  cot 315 degrees

this angle is in the 4th quadrant where tan and cot  are negative

cot 315 = 1 / tan 315 = - 1/ tan 45 =  =  -1

The value of expression cot 675° is, - 1

We have to given that,

To find the value of cot 675°.

Now, We can find the value as,

⇒ cot 675°

⇒ cot (2 × 360 - 45)°

⇒ - cot 45°

⇒ - 1

Hence, The value of expression cot 675° is, - 1

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I need help with #12. I have to show work too.

Answers

Answer: SR is 69 units long.

------------------------------------------------------------
------------------------------------------------------------

Explanation/Work Shown:

SR is the distance from R to S (or S to R; order doesn't matter). In other words, it's the length of segment SR. In this case, SR = 7x-8 for now. Your teacher wants you to find a numeric value for SR. To do that, we need to find x first.

ST is a similar story: it's the length of segment ST. In this case, ST is the algebraic expression 3x-5. 
Finally, RT = 8x+9

So far we have these three equations:
SR = 7x-8
ST = 3x-5
RT = 8x+9

Because SR and ST combine to form RT (and because S is on line RT), this means we can say
SR + ST = RT
by the segment addition postulate

Let's plug in the equations found earlier to get...
SR + ST = RT
(7x-8) + ST = RT ... replace SR with 7x-8
(7x-8) + (3x-5) = RT ... replace ST with 3x-5
(7x-8) + (3x-5) = 8x+9 ... replace RT with 8x+9

Now let's solve for x
(7x-8) + (3x-5) = 8x+9
7x-8 + 3x-5 = 8x+9
(7x+3x)+(-8-5) = 8x+9
10x-13 = 8x+9
10x-13+13 = 8x+9+13 ... add 13 to both sides
10x = 8x+22
10x-8x = 8x+22-8x ... subtrat 8x from both sides
2x = 22
2x/2 = 22/2 ... divide both sides by 2
x = 11

Now that we know x, we can find the length of SR
SR = 7x-8
SR = 7*x-8
SR = 7*11-8 ... replace x with 11 (since x = 11)
SR = 77-8
SR = 69

How many times as heavy is the Golden Eagle as the Red Tailed Hawk? The Golden Eagle weighs 13 9/10 lbs and the red tailed hawk weighs 3 1/2 lbs?

Answers

In order to figure out the ration of the Golden Eagle to the Red Tailed Hawk you would need to convert their numbers a decimal. In this case you would convert 13 9/10lbs to 13.9 and 3 1/2lbs to 3.5. So now you would divide 13.9 by 3.5 and you get 3.9. So in other words you could have 3.9 Red Tailed Hawks to make one Golden Eagle. So the Golden Eagle is 3.9 times heavier than the Red Tailed Hawk.
Final answer:

The Golden Eagle, weighing 13.9 lbs, is approximately 4 times as heavy as the Red Tailed Hawk, which weighs 3.5 lbs.

Explanation:

To find out how many times as heavy the Golden Eagle is compared to the Red Tailed Hawk, we need to divide the weight of the Golden Eagle by the weight of the Red Tailed Hawk. The Golden Eagle weighs 13 9/10 lbs, which can be converted into an improper fraction as 139/10 or a decimal as 13.9 lbs. The Red Tailed Hawk weighs 3 1/2 lbs, which can be converted into an improper fraction as 7/2 or a decimal as 3.5 lbs.

To perform the division, we'll use the decimal form of the weights:

Golden Eagle: 13.9 lbsRed Tailed Hawk: 3.5 lbs

Dividing the Golden Eagle's weight by the Red Tailed Hawk's weight:

13.9 lbs ÷ 3.5 lbs = 3.9714 (approximately)

So, the Golden Eagle is approximately 4 times as heavy as the Red Tailed Hawk.

What types of triangles can have an obtuse angle?

Scalene
Right
Acute
Isosceles

Answers

Scalene = yes it is possible (example: 105 degrees, 5 degrees, 70 degrees)

Right = No, the reason why is because the remaining angles must add to 90 which is less than a right angle. So it's impossible to have one angle over 90 degrees. 

Acute = Also no. All three angles are less than 90 degrees

Isosceles = Yes. It is possible. One example would be 120 degrees, 30 degrees, 30 degrees.
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