Free Printable Logarithms and Logarithmic Functions

1.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

2.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

3.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

4.

Which equation is the inverse of the equation above?

$f\left(x\right)=\log_3x$

a)

$f^{-1}\left(x\right)=3^x$

b)

$f^{-1}\left(x\right)=\log_x3$

c)

$f^{-1}\left(x\right)=x^3$

d)

$f^{-1}\left(x\right)^{ }=3^{-x}$

5.

Write in logarithmic form:
4⁵ = 1024

a)

log ₄ 1024 = 5

b)

log ₅ 1024 = 4

c)

log ₄ 5 = 1024

d)

log ₅ 4 = 1024

6.

Solve for x:

$\log_4x=3$

a)

$4$

b)

$12$

c)

$32$

d)

$64$

7.

Find the approximate value of the logarithmic expression. Round your answer to the nearest whole number:

$\log_{10}1026$

(a)

8.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

9.

Evaluate: $\log_6\ \frac{1}{216}=x$

a)

$x=3$

b)

$x=\frac{1}{3}$

c)

$x=-\frac{1}{3}$

d)

$x=-3$

10.

Write an exponential function in the form $y=ab^{x\ }$ whose graph passes through (1, 8) and (3, 32).

a)

$y=2\left(4\right)^{x\ }$

b)

$y=4\left(2\right)^x$

c)

$y=4\left(\frac{1}{2}\right)^{\ x}$

d)

$y=2\left(\frac{1}{4}\right)^{x\ }$

11.

Write an exponential function in the form $y=ab^{x\ }$ whose graph passes through (1, 1) and (4, 8).

a)

$y=2^{x\ }$

b)

$y=2\left(2\right)^{x\ }$

c)

$y=2\left(\frac{1}{2}\right)^{x\ }$

d)

$y=\frac{1}{2}\left(2\right)^{x\ }$

12.

Find the value of x.

$\frac{1}{2}=\log_9x$

a)

$-3$

b)

$3$

c)

$\frac{1}{3}$

d)

$-\frac{1}{3}$

13.

Find the value of x.

$\frac{1}{3}=\log_x4$

a)

$x=64$

b)

$x=12$

c)

$x=81$

d)

$x=16$

14.

Find the value of x.

$\log_x\ \frac{1}{8}=-3$

a)

$x=-3$

b)

$x=3$

c)

$x=-2$

d)

$x=2$

15.

FInd the inverse of

$f\left(x\right)=\log_{ }\left(\frac{x}{3}\right)$

a)

$f^{-1}\left(x\right)=3\left(10^y\ \right)$

b)

$f^{-1}\left(x\right)=10^y\$

c)

$f^{-1}\left(x\right)=30^y\$

d)

$f^{-1}\left(x\right)=10\left(3^y\ \right)$

16.

Find the inverse of

$y=\ln\left(x-5\right)$

a)

$y=e^x+5$

b)

$y=e^x-5$

c)

$y=5e^x$

d)

$y=-5e^x$

17.

The wind speed s (in miles per hour) near the center of a tornado can be modeled by $s=93\log d+65$ where d is the distance (in miles) that the tornado travels.

A tornado traveled 35 miles. Estimate the wind speed near the center of the tornado.

a)

$s=208.6\ \frac{mi}{h}$

b)

$s=200.8\ \frac{mi}{h}$

c)

$s=206.8\ \frac{mi}{h}$

d)

$s=286.0\ \frac{mi}{h}$

18.

The wind speed s (in miles per hour) near the center of a tornado can be modeled by $s=93\log d+65$ where d is the distance (in miles) that the tornado travels.

The wind speed near the center of a tornado was 150 miles per hour. Find the distance that the tornado traveled.

a)

$d=6.8\ miles$

b)

$d=8.2\ miles$

c)

$d=9\ miles$

d)

$d=86\ miles$

19.

The decibel level D of sound is given by the equation $D=10\log\left(\frac{I}{10^{-12}}\right)$ where I is the intensity of the sound. What is the decibel level when the intensity of the sound is $10^{-8}$ ?

a)

$D=4\ decibels$

b)

$D=10\ decibels$

c)

$D=40\ decibels$

d)

$D=1000\ decibels$

20.

The decibel level D of sound is given by the equation $D=10\log\left(\frac{I}{10^{-12}}\right)$ where I is the intensity of the sound. The pain threshold for sound is 125 decibels. Does a sound with an intensity of $10^{-3}$ exceed the pain threshold? Explain. Attach your explanation.

(a)

21.

$M=\frac{2}{3}\log E-9.9$

Find the inverse of the given function. Describe what the inverse represents. (image from BigIdea Math)

4 lines

22.

Find the inverse of

$y=13+\log x$

a)

$y=10^{\left(x+13\right)}$

b)

$y=10^{\left(x-13\right)}$

c)

$y=10^x+13$

d)

$y=10^x-13$

23.

Find the inverse of $y=e^{\left(x-4\right)}$

a)

$y=\ln x-4$

b)

$y=\ln x+4$

c)

$y=\ln\left(x+4\right)$

d)

$y=\ln\left(x-4\right)$

24.

Rewite the expression in exponential form

$\log_{\frac{1}{3}}27=-3$

a)

$3^{-3}=27$

b)

$\left(\frac{1}{3}\right)^{-3}=27$

c)

$\left(\frac{1}{3}\right)^3=-27$

d)

$\left(-3\right)^{\frac{1}{3}}=27$

25.

Evaluate $\log_749^x$

a)

$2x$

b)

$7x$

c)

$x$

d)

$2$

Logarithms and Logarithmic Functions

Total questions: 25

Worksheet time: 1hrs 23mins

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