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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

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success 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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