Mathematics College

how to solve an equation for x with natural log of x

Answers

Answer 1
Question is not specific, so can only give a general answer.
As an example:
If the equation is of the form
log(x)=5
then raise each side to the power of e to give
e^(log(x))=e^5
Since e^(log(x))=x, we have
x=e^5.
Answer 2

A logarithmic equation involving natural logarithms can be solve by taking the exponent of both sides

How to solve a natural logarithmic equation for x

To solve an equation involving the natural logarithm of x, you generally follow these steps:

Isolate the natural logarithm termExponentiate both sidesSolve for x: After removing the natural logarithm, solve the resulting equation for x.

Take for instance, the equation is of the form

2 + ln(x) = 7

Isolate the natural logarithm

ln(x) = 5

Take the exponent of both sides

So, we have

[tex]x = e^5[/tex]

Evaluate the exponent

x = 148.41

Hence, the logarithmic equation solved for x is x = 148.41

Related Questions

D is the midpoint of CE.E has coordinates (-3,-2), and D has coordinates (2 1/2, 1). Find the coordinate of C.

Answers

midpoint formula : (x1 + x2) / 2, (y1 + y2) / 2
(-3,-2)....x1 = -3 and y1 = -2
(x,y)......x2 = x and y2 = y
now we sub
(-3 + x) / 2, (-2 + y) / 2

(-3 + x) / 2 = 2 1/2
-3 + x = 5/2 * 2
-3 + x = 5
x = 5 + 3
x = 8

(-2 + y) / 2 = 1
-2 + y = 1 * 2
-2 + y = 2
y = 2 + 2
y = 4

so the coordinates of point C are : (8,4)

The coordinate of point C on line CE will be (8, 4).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

D is the midpoint of CE.

E has coordinates (-3,-2), and D has coordinates (2 1/2, 1).

Now, By the definition of midpoint;

Let the coordinate of point C = (x, y)

Then,

((x + (-3))/2 , (y + (-2))/2) = (2 1/2, 1)

By comparison we get;

x + (-3) / 2= 2 1/2

x - 3 = 2 (5/2)

x - 3 = 5

x = 3 + 5

x = 8

And, (y + (-2))/2 = 1

y - 2 = 2

y = 2 + 2

y = 4

Thus, The coordinate of point C = (x, y) = (8, 4)

So, The coordinate of point C on line CE will be (8, 4).

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What is the expanded notation for 2.918?

Answers

 2 + 0.9+ 0.01+ 0.008

I hope this helps.

605 mi in 11 hours at the same rate how many miles would he drive in 13 hours

Answers

First you need to find the unit rate

605/ 11= 55

55*13=715

In 13 hours, 715 miles will be traveled

Simplify each expression (combine like terms)

17x+12-13x

-35+17-3w+12w

Answers

the first one is 4x+17 and the second one is 9w-18
For the first one the answer is 4x+12



And for the second one - 18+9w

What is the unit rate for 822.6 km in 18 hours? Enter your answer, as a decimal, in the box. Please Help

Answers

unit rate = 822.6 / 18 = 45.7

answer
unit rate = 45.7 km per hour
Find the unit rate by dividing 822.6 km by 18 hours:

822.6 km
-------------- = 45.7 km/hr
 18 hrs

Note:  this is approx         45.7 km/hr        0.625 mile
                                         --------------- * ----------------- = 28.6 mph 
                                                 1                   1 km

how can I adjust a quotient to solve a division problem

Answers

Ask them to first estimate the quotient and then to find the actual

what 5x(4+gy) if x= 1 g= 20 Y=14
please show work

Answers

To solve this one, we'll plug in the given x, g, and y values:
[tex]5x(4+gy)[/tex]
[tex]5(1)(4+(20)(14))=5(4+280)=5(284)=1420[/tex]
5•1(4+20•14) =1420 bc 20 • 14 is 280 + 4 = 284 • 5 is 1420

If the radius of a circle measures 2 inches, what is the measure of its diameter?

Answers

the diameter of the circle would be 4 inches
The diameter will equal 4 inches because the radius is half of the diameter...hope this helps..Good luck!

~~Alexis

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(t) = at2 + bt + c, where a, b, and c are to be determined.

Answers

The particular quadratic solution to the ODE is found as follows:

[tex]x=at^2+bt+c[/tex]
[tex]x'=2at+b[/tex]

[tex](2at+b)+2(at^2+bt+c)=t^2+4t+7[/tex]
[tex]2at^2+(2a+2b)t+(b+2c)=t^2+4t+7[/tex]

[tex]\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4[/tex]

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

[tex]x'+2x=0\implies r+2=0\implies r=-2[/tex]

so that [tex]x_c=Ce^{-2t}[/tex] is a characteristic solution to the ODE, and the general solution would be

[tex]x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4[/tex]

To find a, b, c for the solution:

Let's start by writing down the expression for the function x(t) and its derivative:

We have:

x(t) = at² + bt + c
and
x'(t) = 2at + b

Using x' and x into the differential equation x′ + 2x = t² + 4t + 7 gives us:

2at + b + 2*(at² + bt + c) = t² + 4t + 7
Expanding this gives:
2at² + 2bt + b + 4at + 2c = t² + 4t + 7

By equating the coefficients of equivalent powers of t on both sides, we get three equations:

For t² :
2a = 1
So, a = 1/2

For t:
2b + 4a = 4
Substitute a = 1/2 into the equation gives b = 1 - 2 = -1

For the constant term:
b + 2c = 7
Substituting b = -1 gives c = 4.

So the solution is a = 1/2, b = -1, c = 4.

So the specific solution of this differential equation is given by x(t) = (1/2)t² - t + 4.

Start at 5. Create a pattern that multiplies each number by 3 and subtracts 2. Stop when you have 5 numbers.

Answers

without subracting 2 from 5 i have 12, 34, 100, 298, and 892, but with subracting 2 from 5, I have 3, 7, 19, 55, 169 since i was kinda confused

Answer: The required pattern is 13, 37, 109, 325, 973

Step-by-step explanation:

Since, each number in the sequence follows the following rule,

2 less than the 3 times of the previous number.

If we start from 5,

Then first number of the sequence = 3×5 - 2 = 15 - 2 = 13

Second number = 3× 13 - 2 = 39 - 2 = 37

Third number = 3× 37 - 2 = 111 - 2 = 109

Fourth number = 3×109 - 2 = 327 - 2 = 325

Fifth number = 3× 325 - 2 = 975 - 2 = 973

Hence, The required sequence is,

13, 37, 109, 325, 973

Every two years, a manufacturer's total yearly sales decline 20%. She sells 400 total units in her first year. Rounded to the nearest unit, how many total units will she sell her ninth year?

Answers

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ p=period \end{cases}[/tex]

we know, the first year she sold 400 units, thus year 0, 400 units, t = 0, A = 400.

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &400\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ p=period \end{cases} \\\\\\ 400=I(1-r)^{\frac{0}{p}}\implies 400=I\cdot 1\implies 400=I[/tex]

therefore then

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &400\\ r=rate\to 20\%\to \frac{20}{100}\to &0.20\\ t=\textit{elapsed time}\\ p=period\to &2 \end{cases} \\\\\\ A=400(1-0.2)^{\frac{t}{2}}[/tex]

now, how many units will it had decreased by the 9th year?  t = 9

[tex]\bf A=400(1-0.2)^{\frac{9}{2}}[/tex]

146.54 units are the total units will she sell her ninth year.

Here, we have,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

where,

A = amount

I = initial amount

r = rate

t = time

p = period

we know, the first year she sold 400 units,

thus year 0, 400 units, t = 0, A = 400.

so, we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

=> 400 = I × 1

=> 400 = I

therefore then, when, rate = 20 %

we get,

periodic exponential decay is:

[tex]A = I(1-r)^{t/p}[/tex]

[tex]= > A = 400(1-0.2)^{t/2}[/tex]

now, how many units will it had decreased by the 9th year?  t = 9

so, we get,

[tex]= > A = 400(1-0.2)^{9/2}[/tex]

=> A = 146.54

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4r+3=r+21

How do I do this?

Answers

You first:
4r+3-3=r+21-3
4r=r+18 
4r-r=r-r+18
3r=18
3r/3=18/3
r=6
remember that what you do in one side, do it in the other
simplify: 4r + 3 = r + 21, then reorder the terms: 3 + 4r = r + 21.
Reorder the terms 3 + 4r = 21 + r. Solve: 3 + 4r = 21 + r. 
Move all terms containing r to the left, all other terms to the right.
Solving for variable 'r'.
 Add '-1r' to each side of the equation. 3 + 4r + -1r = 21 + r + -1r.
 Combine like terms: 4r + -1r = 3r3 + 3r = 21 + r + -1r
 Combine like terms: r + -1r = 0 3 + 3r = 21 + 0 3 + 3r = 21
 Add '-3' to each side of the equation. 3 + -3 + 3r = 21 + -3
 Combine like terms: 3 + -3 = 0 0 + 3r = 21 + -3 3r = 21 + -3
 Combine like terms: 21 + -3 = 18 3r = 18
Divide each side by '3'. r = 6 Simplifying r = 6

What is the completely factored form of x3 – 64x? x(x – 8)(x – 8) (x-4)(x2+4x+16) x(x – 8)(x + 8) (x – 4)(x + 4)(x + 4)

Answers

After factoring x from both terms, you can factor the difference of two squares.

= x(x² -64)

= x(x -8)(x +8)

_____

It is worth remembering the "speciall form" that is the difference of two squares:

... a² - b² = (a -b)(a +b)

Answer:

x(x -8)(x +8)

Step-by-step explanation:

Rochelle found the quotient of an integer, x, and 13. Is her quotient a rational number

Answers

It helps, in this case, to ask what exactly a rational number is, and how they come up. The various number systems we work with in math come up in response to different kinds of algebraic problems. The natural numbers (sometimes abbreviated N) are the most basic, and they include all of the "counting numbers" you learn in early gradeschool - 1, 2, 3, 4, etc. - and occasionally 0. If we add or multiply any two natural numbers together, we get another natural number, so we don't need to worry about creating any new numbers when we're just working with those operations. Subtraction poses a few issues, though. If we take an expression like 3 - 4, our answer is going to be outside of N. Rather than throwing our hands up and calling it a day at this point, we create a new set of numbers to deal with this situation.

The integers (abbreviated Z) contain all of the natural numbers, and add negative numbers, too (-1, -2, -3, etc.). Multiplication, addition, and subtraction work fine now, and no matter which integers we use, those operations will always give us back another integer. It's not all perfect, though; division gives us a bit of a hassle now. Expressions like 6/3 are fine, since they just produce another integer (2, in this case), but there's no integer result for something like 2/5 or 3/8, so again, we have to create a new set of numbers to compensate.

That set of numbers is what we refer to as the rational numbers (abbreviated Q), named after the fact that all of them are expressed as ratios. By expanding our number system with these, we gain the ability to express every integer as a rational number by putting it over 1 (6 = 6/1, 5 = 5/1, etc.).

So, getting back to the original question, "is the quotient of an integer x and 13 a rational number?" Yes. The quotient of two integers can always be represented as a rational number.

2005 months = how many liters

Answers

Hello!

I think you meant mililiters instead of months.

1 ml = 0.001 L

2005 ml = 2.005 L

And there's your answer! ^

I hope you found this helpful c:

What's 24.67 to one significant figure?

Answers

24.67 is just barely before 25.00, so we should be able to round 20.00, which gives us only one significant digit.

What can be used as a reason in a two-column proof?
Select each correct answer.
conjecture
postulate
definition
premise

Answers

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.

Therefore, what can be used as a reason in a two-column proof are:

Postulates

Definitions

Answer:

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.

Therefore, what can be used as a reason in a two-column proof are:

Postulates

Definitions

A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form? A=–n2 + 3n + 5 B=n2 + 6n + 1 C=2n2 + 6n – 1 D=3n2 + 5

Answers

A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form?      We want (n)(2n+6) - (n^2-1).  (Please note: n^2 is correct, while n2 is not.)

Multiplying out the first term:  2n^2 + 6n 
Subtracting n^2-1:                 - (n^2 -1)
                                             ----------------------
                                                  n^2 + 6n + 1     (answer) 

Answer:

B

Step-by-step explanation:

"unable to determine because x can't take on the value 5.5"

Answers

                    k
   f(x) = -------------------
                x - (5.5)

is an example where there's no finite limit if x approaches 5.5.

steps to solve this equation 25 1/7- 12 5/7=

Answers

[tex] \frac{25*7+1}{7} - 12 \frac{5}{7} [/tex]

[tex] \frac{175+1}{7} - 12 \frac{5}{7} [/tex][tex] \frac{176}{7} - \frac{12*7+5}{7} [/tex]

To solve the equation 25 1/7 - 12 5/7, subtract the whole numbers and fractions separately, and combine them back into a mixed number to get the solution, which is 12 3/7

To solve the equation 25 1/7 - 12 5/7, follow these steps:

First, break the mixed numbers into whole numbers and fractions: (25 + 1/7) - (12 + 5/7).Next, subtract the whole numbers: 25 - 12 = 13.Subtract the fractions: 1/7 - 5/7. Since the denominators are the same, simply subtract the numerators: 1 - 5 = -4. This gives us -4/7, but since we can't have a negative fraction in this context, we'll take 1 away from the whole number 13 and convert it to 7/7, to make the equation easier to solve.Now you have 12 (since we took 1 from 13) and 7/7 - 4/7, which equals 3/7.Add the whole number and the fraction: 12 + 3/7 = 12 3/7.

The solution to the equation is 12 3/7

Alan sells custom made kites online. He makes a flat profit of $20 per kite, but he pays $20 per day for his website. Write an inequality that gives the number of kites Alan needs to sell to make at least $900 per week?

Answers

20x+20y=900
I hope that helps. You'll have to isolate each variable. X= kite, y=website.

Profit on each kite that Allan sells= $ 20 per kite

Amount paid by Allan for his Website = $ 20 per day

Let number of kites sold by Allan per day = x

In 7 days , number of kites sold = 7 x

Amount paid by Allan for his Website in 7 seven days = 20 × 7=$140

We have to make an equality describing number of kites Alan needs to sell to make at least $900 per week.

The Inequality is

→20×7 x -140 ≥ 900

→ 140 x ≥ 900 + 140

→ 140 x ≥1040

→ 7 x ≥ 52 (Minimum number of kites that allan should sell in a week)

Dividing both sides by 140,we get

→ x ≥ [tex]\frac{1040}{140}=7.43[/tex]= 8 kites in a day(approx)




Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches.

A) 36π in. ^ 3
B) 48π in. ^ 3
C) 52π in. ^ 3
D) 64π in. ^ 3

Answers

B is the correct answer

Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?

Answers

Compute for the total balance:

total balance = $415 + $215 = $630

 

Then we compute for the total credit limit:

total credit limit = $1,000 + $750 = $1,750

 

The credit utilization would simply be the percentage ratio of total balance over total credit limit. That is:

credit utilization = ($630 / $1,750) * 100%

credit utilization = 36%

Forty percent of the players on a soccer team are experienced players. The coach wants to increase this percent. There are 10 players on the team now. The expression below represents the percent of experienced players on the team after the coach adds x experienced players.

100(x+4)/x+10

What is:
a. Original ratio of experienced to total players
b. Final ratio of experienced to total players
c. Final total number of players

Choices

4/10
x+10
4
10
x+4/x+10

Answers

Part A:

Given that forty percent of the players on a soccer team are experienced players.

Then, the original ratio of experienced to total players is given by 40/100 = 4/10



Part B:

Given that the expression [tex] \frac{100(x+4)}{x+10} [/tex] represents the percent of experienced players on the team after the coach adds x experienced players.

Then, the final ratio of experienced to total players is given by:

[tex] \frac{\frac{100(x+4)}{x+10}}{100} =\frac{x+4}{x+10}[/tex]



Part C:

Given that there are 10 players on the team now, and that the coach adds x experienced player, then the number of players on the team now is given by:

10 + x.

What is the answer to the problem below?

Solve the system of equations graphically.

x=3
y=4

Answers

Hi there!

They already give us the answer, which is (3,4). So all we have to do is graph it on the graph. 3 is for x and 4 is for y.

Check the picture below.
Here we're given the solution on a silver platter:

(3,4)

You could solve this graphically by graphing the vertical line x = 3 and the horiz. line y = 4.  A visual check would show that these two lines intersect at (3,4).

Can I have help on number 16 and please explain how you got the answer

Answers

The area of the rectangle is defined as its length multiplied by its width. This rectangle has a length of 3 ft and a width of (c + 4) ft, so its area would be [tex]3(c+4)[/tex] feet. Using the distributive property, we can simplify this to:

[tex]3c+3(4)\\ 3c+12[/tex]

So the area of this particular rectangle would be 3c + 12 sq. ft

$185 DVD player 6% markup

Answers

$196.10 dbdhdbrbhtbt
after the markup it will be 196.1$

i think.....
 
if it is right dont forget to give me brainliest

DOES ANYONE HAVE A WORD PROBLEM FOR [5+10] DIVIDED BY 5 this is 5th grade math by the way

Answers

The answer is going to be (5+10)/5. Hope that helped
Billy's mom bought 5 pieces of candy in one store and 10 more pieces of the same candy in another store. Billy had 4 friends with him, so there are 5 kids altogether. His mother wants to distribute the candy by all the kids. How many pieces of candy does each kid get?

what is the answer of 9X23+3X39-28=n

Answers

9x23+3x39-28=n


n= 296

Answer: n=296

Step-by-step explanation: 9 x 23 + 3 x 39 - 28 + n = 296  

Hope this helps! <3

How do you figure out what 1/10 of 1,7000.000 km squared is?

Answers

The first thing you would do is square 17,000, which is 298,000,000. Then you would multiply 298,000,000 by 0.10. (or divide the number by 10)

This would get you 28,900,000.
Other Questions
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