<< Chapter < Page Chapter >> Page >

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
Got questions? Get instant answers now!

Logarithmic Functions

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

17 x = 4913

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

log a b = 2 5

Got questions? Get instant answers now!

Rewrite e 3.5 = h as an equivalent logarithmic equation.

Got questions? Get instant answers now!

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

x = 64 1 3 = 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

log ( 0 .000001 ) = 6

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Evaluate ln ( e 0.8648 ) without using a calculator.

ln ( e 0.8648 ) = 0.8648

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Graphs of Logarithmic Functions

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


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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 ) .

Got questions? Get instant answers now!

Logarithmic Properties

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

Got questions? Get instant answers now!

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

log 8 ( 65 x y )

Got questions? Get instant answers now!

Rewrite log m ( 67 83 ) in expanded form.

Got questions? Get instant answers now!

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

ln ( z x y )

Got questions? Get instant answers now!

Rewrite ln ( 1 x 5 ) as a product.

Got questions? Get instant answers now!

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

log y ( 12 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

Rewrite log 3 ( 12.75 ) to base e .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Exponential and Logarithmic Equations

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

Got questions? Get instant answers now!

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

x = 3

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

no solution

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x = ln ( 11 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

a = e 4 3

Got questions? Get instant answers now!

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 .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Questions & Answers

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
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask