Free Printable Unit 3 Exam Review

1.

Determine the domain of $g\left(x\right)=\log_3\left(4x-2\right)$ ?

a)

( $\frac{2}{4}$ ,∞)

b)

(-∞, $\frac{2}{4}$ )

c)

(-∞,∞)

d)

( $\frac{4}{2}$ ,∞)

2.

Use properties of the logarithms to simplify the expression below into a single logarithm. Assume that all variables represent positive real numbers. $5\log_3X-\log_3Y+\frac{1}{5}\log_3Z$

a)

$\log_3\frac{\sqrt[5]{X^5}}{Y}$

b)

$\frac{\log_3X^5\sqrt[5]{Z}}{\log_3Y}$

c)

$\frac{\log_35X\sqrt[5]{Z}}{Y}$

d)

$\log_3\frac{X^5\sqrt[5]{Z}}{Y}$

3.

Simplify: $\log_216+\log_28$

a)

- 16

b)

7

c)

-2

d)

8

4.

Consider a function g(x) such that $\lim_{x\rightarrow-\infty}\ g\left(x\right)=\infty$ and $\lim_{x\rightarrow\infty\ }g\left(x\right)=0$ . Which of the following functions could be g(x)?

a)

$2\left(\frac{1}{4}\right)^X$

b)

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

c)

$\log_3\left(X\right)-2$

d)

$5e^x-18$

5.

Determine the following statement that best describes the transformation of the graph of the parent function $f\left(x\right)=\log\ x$ into the graph of $g\left(x\right)=\log_{ }\left(\frac{1}{2}x-4\right)+3$ ?

a)

Horizontal stretch of 2, translate 8 units to the right, translate 3 units up.

b)

Horizontal compression of 8, translate 4 units to the left, 3 units up.

c)

Horizontal compression of 8, translate 12 units to the left, translate 3 units up.

d)

Horizontal stretch of 2, translate 12 units to the left, translate 3 units up.

6.

How many solutions are there to the following logarithmic equation?

$\log_3\left(x+1\right)+\log_3\left(x-2\right)=\log_39$

a)

No solution

b)

One Solution

c)

Two solution

d)

Three solution

7.

Determine the following that best describes the graph of $f\left(x\right)=e^{-x}+4$ ?

a)

x-intercept at the origin, $\lim_{x\rightarrow\infty}f\left(x\right)=4$ , f(x) is even

b)

y-intercept at (0,5), $\lim_{x\rightarrow\infty}f\left(x\right)=4$ , f(x) is neither even nor odd

c)

y-intercept at (0,5), $\lim_{x\rightarrow\infty}f\left(x\right)=\infty$ , f(x) is neither even nor odd

d)

y-intercept at (0,5), $\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ , fx is neither even nor odd

8.

Evaluate the properties of logarithms to expand the expression below into multiple logarithms. Assume that all variables represent positive real numbers. $\ln\left(\frac{\sqrt[4]{x}}{y^8}\right)$

a)

$\frac{1}{4}\ln x-8\ln y$

b)

$\frac{1}{4}\ln x+8\ln y$

c)

$4\ln x-8\ln y$

d)

$4\ln x+8\ln y$

9.

What is the inverse function of $f\left(x\right)=6^x$ ?

a)

$g\left(x\right)=6^{-x}$

b)

$g\left(x\right)=\log_6x$

c)

$g\left(x\right)=6^{\frac{1}{x}}$

d)

$g\left(x\right)=-6^x$

10.

Let $g\left(x\right)=3^{-x}+5$ , determine which of the following about g(x) must be true? I. The graph of g(x) is increasing on (-∞, ∞). II. There are no local or absolute extrema on the graph of g(x). III. The graph is bounded below.

a)

II only

b)

II and III only

c)

I and II only

d)

I and III only

11.

Jennifer deposits $5,000 in a savings account with an annual interest rate of 4%. How long will it take for her account balance to reach $10,000 if the interest is compounded monthly?

$A=P\left(1+\frac{r}{n}\right)^{nt}$

a)

17.672 years

b)

18.245 years

c)

17.357 years

d)

18.123 years

12.

The population P (in millions) of a bacteria farm in Texas from 2025 through 2035 can be approximated by the model $P\left(t\right)=30.5e^{0.0395t}$ where t represents the year, with t=1 corresponding to 2026. According to this model, what year will the bacteria reach 62 million?

a)

2043

b)

2040

c)

2035

d)

2025

13.

Determine each of the following exponential or logarithmic equations algebraically.

$\log\left(x+4\right)+\log\left(3\right)=\log8x$

a)

$x=\frac{5}{12}$

b)

$x=\frac{12}{5}$

c)

$x=\frac{4}{3}$

d)

$x=\frac{3}{4}$

14.

Determine each of the following exponential or logarithmic equations algebraically.

$e^{2x}-6e^x=27$

a)

x=ln 2

b)

x =ln 3

c)

x = ln 6

d)

x = ln 9

15.

Determine each of the following exponential or logarithmic equations algebraically.

$2^{x+7}=32^{-4}$

a)

x = -14

b)

x = -27

c)

x = -8

d)

x = -72

Unit 3 Exam Review

Total questions: 15

Worksheet time: 1hrs 15mins

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