how do logarithms work
A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:
log 100 = 2
because
102 = 100
This is an example of a base-ten logarithm. We call it a base ten logarithm because ten is the number that is raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. If you wanted, you could use two as a base unit. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight:
log2 8 = 3
because
23 = 8
In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written
log
and a base ten logarithmic equation is usually written in the form:
log a = r
A natural logarithm is written
ln
and a natural logarithmic equation is usually written in the form:
ln a = r
So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.
Final answer:
Logarithms are used in Mathematics to solve exponential equations by converting them into linear equations. They involve finding the exponent to which a base must be raised to equal a given number. Properties of logarithms, such as the product and quotient rules, help manipulate and solve logarithmic equations.
Explanation:
Logarithms are mathematical tools used to solve exponential equations and simplify complex calculations. They are the inverse function of exponential functions and help us solve for the unknown exponent in an equation.
Logarithms work by converting exponential equations into linear equations. When we take the logarithm of a number, we are finding the exponent to which a base must be raised to equal that number. For example, the logarithm (base 10) of 100 is 2, because 10 raised to the power of 2 equals 100.
The properties of logarithms allow us to manipulate them to solve equations. Some key properties include:
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.The florist has 63 roses and carnations. If she has 27 roses how many carnations does she have?
Miss Martin has 7000 in her savings account. Alonso has 1/10 as much money in his account as Miss Martin. How much money does Alonso have in his account.
A bank offers a CD that pays a simple interest rate of 6.0. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 6 years.
Based upon a long period of record keeping the following represents the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.
x 0 1 2 3 4 5 6
p(x) .08 .17 .21 k .21 k .13
a. What is the value of k?
b. Calculate the expected value of x.
c. Calculate the expected value of x^2
.
d. Calculate the variance of x.
e. Calculate the standard deviation of x
f. Calculate the variance of 3x.
g. Suppose that network slowness is independent from week to week. What is the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks?
h. Calculate the variance of the random variable x^2
Answer:.1
Step-by-step explanation:
Nicolas has three fewer than twice the number of songs downloaded as Sabrina does. Interpret the meaning of the expression 2x – 3. The expression 2x – 3 represents
The expression 2x-3 represent's: The number of songs downloaded by Nicholas.
The variable x represents: The number of songs downloaded by Sabrina.
solve the equation .......x/9 = 2/45 +x/10
if m angel 1 equal 42 and m angle 2 equal 27, then m angle APC equal
The measure of angle APC equals 69°
What is the measure of angle APC?
∠1 = 42°
∠2 = 27°
Angle APC is equal to the sum of angle 1 and angle 2.
∠APC = ∠1 + ∠2
= 42° + 27°
= 69°
Hence, m ∠ APC = 69°
Complete question:
if m ∠ 1 = 42 and m ∠ 2 = 27, then m ∠ APC = ?
You play video games online. When you sign up with the game site, you get 400400 points. You earn 5050 more points for each hour that you play. How many hours do you have to play to get to 1,000 points?
Convert 50 feet per second to miles per hour.
5280 ft = 1 mi
Round to the nearest hundredth.
solve: -3(3x+1)-41>-5(-2x+4)+5x
Answer:
Step-fbccbbby-CBC step explanation:
The number of seats in the first row of a concert hall is 6. The second row has 9seats, the third row has 12 seats, and the fourth row has 15 seats. How many seats are in the eighth row?
A room has an area of 60 square meters and a perimeter of 32 meters what are the length and width of the room
Estimate 508-113 help me please
jake rounded 18,752 to the nearest ten thousand which is his number
Complete te pattern 3,400,000 34,000
how do you solve the following
6/13=3/c
PQR has two known interior angles of 34°, and 80°. △RST has two known interior angles of 24°, and 90°. What can be determined about whether △PQR and △RST are similar?
Answer:
△PQR and △RST are not similar.
Step-by-step explanation:
In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is
[tex]180-34-80=66[/tex]
In triangle △RST, two known interior angles are 24° and 90°.
[tex]180-24-90=66[/tex]
Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.
Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.
You have 16 Yellow beads,20 red beads,and 24 orange beads to make identical bracelets. What is the greatest number of bracelets that you can make using all beads?
The greatest number of identical bracelets that can be made using all the beads is 4. This is found by determining the greatest common divisor (GCD) of 16, 20, and 24, which is 4. Each bracelet will consist of 4 yellow beads, 5 red beads, and 6 orange beads.
Explanation:The subject of this question is the mathematical concept of the greatest common divisor (GCD). In the given problem, you are tasked with finding the maximum number of identical bracelets you can make with a given number of beads. The concept of GCD is used here.
First, we need to determine the GCD of the quantities of the three different colored beads:
16 Yellow beads 20 Red beads 24 Orange beads
The GCD of 16, 20, and 24 is 4. This means the largest number of identical bracelets you can make, using all of the beads, is 4. Each bracelet will have 4 yellow beads, 5 red beads, and 6 orange beads.
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in a student council election Martha and Hillary received a total of 1600 votes, Martha received 81 more votes than Hillary, how many votes did Martha receive
Find the unit rate,Kenny reads 5/8 pages in 2/3 minute.Please show your work.
Mr.chu is slicing 4 cantaloupes for his class.There are 24 students in class. If Me.Chu cut the cantaloupes to make an equal portion for each student , how much of a whole cantaloupe will each student get?
Each student will receive approximately 0.1667 parts of a whole cantaloupe when Mr. Chu evenly divides 4 cantaloupes among 24 students.
Explanation:The subject of this problem is how to divide a quantity fairly between multiple recipients, also known as division. If Mr. Chu is slicing 4 cantaloupes and wants to divide them equally among 24 students, we need to find how much each student would receive.
This is solved by simply dividing the total quantity of cantaloupes by the number of students. So, 4 (whole cantaloupes) divided by 24 (students) equals 0.1667.
Therefore, each student will get approximately 0.1667 of a whole cantaloupe.
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how do you know that the decimal for 2/11 repeats without end
Evaluate the expression below when x = -2. x2 − 8 x + 6
Find the rate of change of q with respect to p when p = 20 q 2 + 5 .
The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.
Explanation:
The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.
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how many inches are equal to 30.48 cm
On an average, the number of students that choose to study arts subjects at greyin tide university is 17 each year.what is the probability that exactly 13 students will take up arts in the coming year?
The probability that exactly 13 students will take up arts in the coming year is; 76.47%
What is the probability?We are given;
Number of students that study art each year = 17
Now, we want to find the probability that 13 students will take up arts in the following year. This is;
P(13 will take art the next year) = 13/17 * 100%
P(13 will take art the next year) = 76.47%
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Which graph represents the solution set of the system of inequalities? {3y≥x−93x+y>−3
That is the correct graph that represents
{3y≥x−9 3x+y>−3
hope i helped =D
we have
[tex]3y\geq x-9[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the solid red line
See the attached figure N [tex]1[/tex]
[tex]3x+y> -3[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the dotted blue line
See the attached figure N [tex]2[/tex]
The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line
See the attached figure N [tex]3[/tex]
therefore
the answer in the attached figure
Solve for x. 2/3x=10 Enter your answer in the box.
Find and sketch the domain of the function. f(x, y, z) = 4 − x2 − y2 − z2
The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].
To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.
In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).
In interval notation, we can express this as:
[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]
This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.
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