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The graph below shows transformations of the graph of f ( x ) = 2 x . What is the equation for the transformation?

Graph of f(x)=2^x
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Logarithmic Functions

Rewrite log 17 ( 4913 ) = x as an equivalent exponential equation.

17 x = 4913

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Rewrite ln ( s ) = t as an equivalent exponential equation.

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Rewrite a 2 5 = b as an equivalent logarithmic equation.

log a b = 2 5

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Rewrite e 3.5 = h as an equivalent logarithmic equation.

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Solve for x log 64 ( x ) = 1 3 to exponential form.

x = 64 1 3 = 4

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Evaluate log 5 ( 1 125 ) without using a calculator.

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Evaluate log ( 0 .000001 ) without using a calculator.

log ( 0 .000001 ) = 6

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Evaluate log ( 4.005 ) using a calculator. Round to the nearest thousandth.

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Evaluate ln ( e 0.8648 ) without using a calculator.

ln ( e 0.8648 ) = 0.8648

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Evaluate ln ( 18 3 ) using a calculator. Round to the nearest thousandth.

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Graphs of Logarithmic Functions

Graph the function g ( x ) = log ( 7 x + 21 ) 4.


Graph of g(x)=log(7x+21)-4.

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Graph the function h ( x ) = 2 ln ( 9 3 x ) + 1.

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State the domain, vertical asymptote, and end behavior of the function g ( x ) = ln ( 4 x + 20 ) 17.

Domain: x > 5 ; Vertical asymptote: x = 5 ; End behavior: as x 5 + , f ( x ) and as x , f ( x ) .

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Logarithmic Properties

Rewrite ln ( 7 r 11 s t ) in expanded form.

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Rewrite log 8 ( x ) + log 8 ( 5 ) + log 8 ( y ) + log 8 ( 13 ) in compact form.

log 8 ( 65 x y )

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Rewrite log m ( 67 83 ) in expanded form.

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Rewrite ln ( z ) ln ( x ) ln ( y ) in compact form.

ln ( z x y )

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Rewrite ln ( 1 x 5 ) as a product.

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Rewrite log y ( 1 12 ) as a single logarithm.

log y ( 12 )

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Use properties of logarithms to expand log ( r 2 s 11 t 14 ) .

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Use properties of logarithms to expand ln ( 2 b b + 1 b 1 ) .

ln ( 2 ) + ln ( b ) + ln ( b + 1 ) ln ( b 1 ) 2

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Condense the expression 5 ln ( b ) + ln ( c ) + ln ( 4 a ) 2 to a single logarithm.

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Condense the expression 3 log 7 v + 6 log 7 w log 7 u 3 to a single logarithm.

log 7 ( v 3 w 6 u 3 )

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Rewrite log 3 ( 12.75 ) to base e .

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Rewrite 5 12 x 17 = 125 as a logarithm. Then apply the change of base formula to solve for x using the common log. Round to the nearest thousandth.

x = log ( 125 ) log ( 5 ) + 17 12 = 5 3

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Exponential and Logarithmic Equations

Solve 216 3 x 216 x = 36 3 x + 2 by rewriting each side with a common base.

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Solve 125 ( 1 625 ) x 3 = 5 3 by rewriting each side with a common base.

x = 3

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Use logarithms to find the exact solution for 7 17 9 x 7 = 49. If there is no solution, write no solution .

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Use logarithms to find the exact solution for 3 e 6 n 2 + 1 = 60. If there is no solution, write no solution .

no solution

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Find the exact solution for 5 e 3 x 4 = 6 . If there is no solution, write no solution .

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Find the exact solution for 2 e 5 x 2 9 = 56. If there is no solution, write no solution .

no solution

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Find the exact solution for 5 2 x 3 = 7 x + 1 . If there is no solution, write no solution .

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Find the exact solution for e 2 x e x 110 = 0. If there is no solution, write no solution .

x = ln ( 11 )

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Use the definition of a logarithm to solve. 5 log 7 ( 10 n ) = 5.

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47. Use the definition of a logarithm to find the exact solution for 9 + 6 ln ( a + 3 ) = 33.

a = e 4 3

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Use the one-to-one property of logarithms to find an exact solution for log 8 ( 7 ) + log 8 ( 4 x ) = log 8 ( 5 ) . If there is no solution, write no solution .

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Use the one-to-one property of logarithms to find an exact solution for ln ( 5 ) + ln ( 5 x 2 5 ) = ln ( 56 ) . If there is no solution, write no solution .

x = ± 9 5

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The formula for measuring sound intensity in decibels D is defined by the equation D = 10 log ( I I 0 ) , where I is the intensity of the sound in watts per square meter and I 0 = 10 12 is the lowest level of sound that the average person can hear. How many decibels are emitted from a large orchestra with a sound intensity of 6.3 10 3 watts per square meter?

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Questions & Answers

give me an example of a problem so that I can practice answering
Jenefa Reply
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
CJ Reply
I want to learn about the law of exponent
Quera Reply
explain this
Hinderson Reply
what is functions?
Angel Reply
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich
If the plane intersects the cone (either above or below) horizontally, what figure will be created?
Feemark Reply
can you not take the square root of a negative number
Sharon Reply
No because a negative times a negative is a positive. No matter what you do you can never multiply the same number by itself and end with a negative
lurverkitten
Actually you can. you get what's called an Imaginary number denoted by i which is represented on the complex plane. The reply above would be correct if we were still confined to the "real" number line.
Liam
Suppose P= {-3,1,3} Q={-3,-2-1} and R= {-2,2,3}.what is the intersection
Elaine Reply
can I get some pretty basic questions
Ama Reply
In what way does set notation relate to function notation
Ama
is precalculus needed to take caculus
Amara Reply
It depends on what you already know. Just test yourself with some precalculus questions. If you find them easy, you're good to go.
Spiro
the solution doesn't seem right for this problem
Mars Reply
what is the domain of f(x)=x-4/x^2-2x-15 then
Conney Reply
x is different from -5&3
Seid
All real x except 5 and - 3
Spiro
***youtu.be/ESxOXfh2Poc
Loree
how to prroved cos⁴x-sin⁴x= cos²x-sin²x are equal
jeric Reply
Don't think that you can.
Elliott
By using some imaginary no.
Tanmay
how do you provided cos⁴x-sin⁴x = cos²x-sin²x are equal
jeric Reply
What are the question marks for?
Elliott
Someone should please solve it for me Add 2over ×+3 +y-4 over 5 simplify (×+a)with square root of two -×root 2 all over a multiply 1over ×-y{(×-y)(×+y)} over ×y
Abena Reply
For the first question, I got (3y-2)/15 Second one, I got Root 2 Third one, I got 1/(y to the fourth power) I dont if it's right cause I can barely understand the question.
Is under distribute property, inverse function, algebra and addition and multiplication function; so is a combined question
Abena

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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