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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

what is the function of sine with respect of cosine , graphically
Karl Reply
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
Aashish Reply
sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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