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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

The average annual population increase of a pack of wolves is 25.
Brittany Reply
how do you find the period of a sine graph
Imani Reply
Period =2π if there is a coefficient (b), just divide the coefficient by 2π to get the new period
Am
if not then how would I find it from a graph
Imani
by looking at the graph, find the distance between two consecutive maximum points (the highest points of the wave). so if the top of one wave is at point A (1,2) and the next top of the wave is at point B (6,2), then the period is 5, the difference of the x-coordinates.
Am
you could also do it with two consecutive minimum points or x-intercepts
Am
I will try that thank u
Imani
Case of Equilateral Hyperbola
Jhon Reply
ok
Zander
ok
Shella
f(x)=4x+2, find f(3)
Benetta
f(3)=4(3)+2 f(3)=14
lamoussa
14
Vedant
pre calc teacher: "Plug in Plug in...smell's good" f(x)=14
Devante
8x=40
Chris
Explain why log a x is not defined for a < 0
Baptiste Reply
the sum of any two linear polynomial is what
Esther Reply
divide simplify each answer 3/2÷5/4
Momo Reply
divide simplify each answer 25/3÷5/12
Momo
how can are find the domain and range of a relations
austin Reply
the range is twice of the natural number which is the domain
Morolake
A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
Diddy Reply
6000
Robert
more than 6000
Robert
can I see the picture
Zairen Reply
How would you find if a radical function is one to one?
Peighton Reply
how to understand calculus?
Jenica Reply
with doing calculus
SLIMANE
Thanks po.
Jenica
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
rachel Reply
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic. Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15) it's standard equation is x^2 + y^2/16 =1 tell my why is it only x^2? why is there no a^2?
Reena Reply
what is foci?
Reena Reply
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
how to determine the vertex,focus,directrix and axis of symmetry of the parabola by equations
Bryssen Reply

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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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