Free Printable 2.2 Assignment: Logarithmic Functions

1.

Express

6^3=216

in logarithmic form.

a)

$\log_3216=6$

b)

$\log_6216=3$

c)

$\log\left(6^3\right)=216$

d)

$\ln\left(6^3\right)=216$

2.

Which of the following gives the correct exponential form for the equation?

\ln x=\pi

a)

$e^{\pi}=x$

b)

$e^x=\pi$

c)

$10^x=\pi$

d)

$10^{\pi}=x$

3.

Express

\log_864

using Change of Base.

a)

$\frac{\ln64}{\ln8}$

b)

$\frac{\log8}{\log64}$

c)

$\log\left(\frac{64}{8}\right)$

d)

$\ln\left(\frac{8}{64}\right)$

4.

Evaluate

\log_520

. Round to the nearest hundredth.

a)

1.46

b)

1.86

c)

4.00

d)

13.98

5.

$\ln4$ is equivalent to which of the following?

a)

$\log\left(\frac{e}{4}\right)$

b)

$\log\left(\frac{4}{e}\right)$

c)

$\frac{\log4}{\log e}$

d)

$\frac{\log e}{\log4}$

6.

Solve for x:

2^x=9

a)

$x=\frac{9}{2}$

b)

$x=\log_29$

c)

$x=\frac{\log2}{\log9}$

d)

$x=\log\left(\frac{9}{2}\right)$

7.

Write

10^{-3}=\frac{1}{1000}

in logarithmic form.

a)

$\log\left(-\frac{1}{3}\right)=\frac{1}{1000}$

b)

$\log_{10}\left(\frac{1}{1000}\right)=-\frac{1}{3}$

c)

$\log_{10}\left(-3\right)=\frac{1}{1000}$

d)

$\log\left(\frac{1}{1000}\right)=-3$

8.

Write

\frac{2}{3}=\log_{64}16

in exponential form.

a)

$64^{\frac{2}{3}}=16$

b)

$64\left(\frac{2}{3}\right)=16$

c)

$16^{\frac{2}{3}}=64$

d)

$\left(\frac{2}{3}\right)^{16}=64$

9.

Solve for x:

e^{x-1}=8

.

a)

$x=1+\ln8$

b)

$x=\ln9$

c)

$x=1+\log8$

d)

$x=\log9$

10.

$f\left(x\right)=3^{x+4}$ . Find $f^{-1}\left(x\right)$ .

a)

$f^{-1}\left(x\right)=\log_3\left(x+4\right)$

b)

$f^{-1}\left(x\right)=\log_3\left(x-4\right)$

c)

$f^{-1}\left(x\right)=\log_3\left(x\right)-4$

d)

$f^{-1}\left(x\right)=\log_3\left(x\right)+4$

11.

Let $f\left(x\right)=\log_2\left(x-6\right)$ . Find the equation of the asymptote of $f\left(x\right)$ .

a)

$y=6$

b)

$x=6$

c)

$x=0$

d)

$y=0$

12.

The graph of a logarithmic function is given. What is the equation of the asymptote of the logarithmic function?

a)

$y=4$

b)

$y=5$

c)

$x=4$

d)

$x=5$

13.

What is the domain of the function $y=\log\left(x-3\right)$ ?

a)

(-∞, +∞)

b)

(3, +∞)

c)

(-3, +∞)

d)

(-∞, 3)

14.

Which of the following logarithmic functions has a domain of (-∞, 1)?

a)

$y=\log_3\left(1-x\right)$

b)

$y=-\log_2\left(x-1\right)$

c)

$y=-\log\left(x-1\right)$

d)

$y=-\ln\left(x\right)+1$

15.

Find the range of $f\left(x\right)=\ln\left(x+2\right)+4$ .

a)

(-∞, +∞)

b)

(-2, +∞)

c)

(-∞, 4)

d)

(-∞, 6)

16.

$f\left(x\right)=\log\left(x-2\right)$ . Which of the following describes the left-hand end behavior of the graph?

a)

As $x\rightarrow2^+$ , $f\left(x\right)\rightarrow-\infty$ .

b)

As $x\rightarrow2^-$ , $f\left(x\right)\rightarrow-\infty$ .

c)

As $x\rightarrow2$ , $f\left(x\right)\rightarrow-\infty$ .

d)

As $x\rightarrow-\infty$ , $f\left(x\right)\rightarrow-\infty$ .

17.

Which of the following describes the right-hand end behavior of the graph?

a)

As $x\rightarrow4^+$ , $f\left(x\right)\rightarrow-\infty$ .

b)

As $x\rightarrow4^-$ , $f\left(x\right)\rightarrow-\infty$ .

c)

As $x\rightarrow4$ , $f\left(x\right)\rightarrow-\infty$ .

d)

As $x\rightarrow+\infty$ , $f\left(x\right)\rightarrow-\infty$ .

2.2 Assignment: Logarithmic Functions

Total questions: 17

Worksheet time: 9mins

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