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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

how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
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Seidu
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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