Free Printable Unit 4 Test #3 Review (Activity 23 & 24)

1.

Which logarithmic equation is equivalent to

16^{\frac{3}{4}}=8

a)

$\log_{\frac{3}{4}}16=8$

b)

$\log_816=\frac{3}{4}$

c)

$\log_{16}\ \frac{3}{4}=8$

d)

$\log_{16}\ 8=\frac{3}{4}$

2.

Which logarithmic equation is equivalent to $3^5=243$ ?

a)

$\log_5\ 243=3$

b)

$\log_{243\ }3=5$

c)

$\log_{243}\ 5=3$

d)

$\log_3\ 243=5$

3.

Which exponential equation is equivalent to $\log_{14}\ \frac{1}{196}=-2$ ?

a)

$\left(\frac{1}{196}\right)^{-2}=14$

b)

$\left(-2\right)^{14}=\frac{1}{196}$

c)

$14^{-2}=\frac{1}{196}$

d)

$\left(-2\right)^{\frac{1}{196}}=14$

4.

Which exponential equation is equivalent to $5^4=625$ ?

a)

$\log_4\ 5=625$

b)

$\log_5\ 4=625$

c)

$\log_5\ 625=4$

d)

$\log_{625}\ 5=4$

5.

Fully expand the logarithm $\log_8\ \left(\frac{x\cdot z}{y^4}\right)^6$

a)

$6\log_8\ x+6\log_8\ z-24\log_{8\ }y$

b)

$6\log_8\ z+6\log_8\ x+24\log_8\ y$

c)

$24\log_8\ x+6\log_8\ y+6\log_8\ z$

d)

$\log_8\ w+\frac{\log_8\ x}{3}+\frac{\log_8\ y}{3}+\frac{\log_8\ z}{3}$

6.

Fully expand the logarithm $\log_5\ \left(\frac{x^2}{y\cdot z}\right)^4$

a)

$8\log_5\ x-4\log_5\ y-4\log_5\ z$

b)

$\log_5\ x+\log_5\ y+\log_5\ w+2\log_5\ z$

c)

$2\log_5\ x-\log_5\ z-4\log_5\ y$

d)

$\log_5\ z+2\log_5\ x-4\log_5\ y$

7.

Condense to a single logarithm $5\log_{8\ }a+10\log_8\ b+5\log_8\ c$

a)

$\log_8\ \frac{ca^2}{b^5}$

b)

$\log_8\ \frac{c^5a^5}{b^{10}}$

c)

$\log_8\ \frac{c^{10}a^{10}}{b^5}$

d)

$\log_8\ \left(c^5b^{10}a^5\right)$

8.

Condense to a single logarithm $3\log x-3\log z-9\log y$

a)

$\log\left(z^3y^3x^9\right)$

b)

$\log\frac{x^3}{z^3y^9}$

c)

$\log\left(xz^3y^3\right)$

d)

$\log\left(z\sqrt{yx}\right)$

9.

Which of the following is equivalent to $\log_4\ 9$ ?

a)

$\log9-\log4$

b)

$\log9+\log4$

c)

$\frac{\log9}{\log4}$

d)

$\frac{\log4}{\log9}$

10.

Which of the following is equivalent to $\log_6\ 2.7$ ?

a)

$\log2.7-\log6$

b)

$\frac{\log2.7}{\log6}$

c)

$\log2.7+\log6$

d)

$\frac{\log6}{\log2.7}$

11.

Solve $4^{-x-2}=64^{-2x+1}$

a)

$-5$

b)

$1$

c)

$-1$

d)

$-\frac{8}{5}$

12.

Solve $81^{2x-1}=3^5$

a)

$4$

b)

$-\frac{5}{4}$

c)

All real numbers

d)

$\frac{9}{8}$

13.

Solve $16^{x+1}-3=5$

a)

No Solution

b)

$-\frac{1}{4}$

c)

$\frac{5}{3}$

d)

$\frac{1}{4}$

14.

Solve $\left(\frac{1}{243}\right)^{2x-3}+7=88$

a)

$\frac{11}{10}$

b)

$-\frac{4}{3}$

c)

$1$

d)

$4$

15.

Which of the following functions is a horizontal translation 6 units to the left and a vertical translation 3 units down from its parent function $f\left(x\right)=\log_3\ x$ ?

a)

$y=\log_3\left(x-6\right)+3$

b)

$y=\log_3\left(x-3\right)+6$

c)

$y=\log_3\left(x+6\right)-3$

d)

$y=\log_3\left(x+3\right)-6$

16.

Which of the following functions is a vertical stretch by a factor of 5, a horizontal translation 4 units to the right and a vertical translation 2 units up from its parent function

\ln x

a)

$y=5\ln\left(x-4\right)+2$

b)

$y=\frac{1}{5}\ln\left(x-4\right)+2$

c)

$y=5\ln\left(x+2\right)-4$

d)

$y=\frac{1}{5}\ln\left(x-2\right)+4$

17.

Given the following logarithmic equation, what is the equation of the asymptote? $y=\log_2\left(x+3\right)-2$

a)

$x=3$

b)

$x=-3$

c)

$y=-3$

d)

$x=-2$

18.

Given the following logarithmic equation, what is the equation of the asymptote? $y=\log\left(x-4\right)+4$

a)

$y=-4$

b)

$y=4$

c)

$x=4$

d)

$x=-4$

19.

Which of the following is the graph of the logarithmic function $f\left(x\right)=\log_2\left(x+2\right)+4$ ?

a)

b)

c)

d)

20.

Which of the following is the graph of the logarithmic function $f\left(x\right)=\log_5\left(x-1\right)+5$ ?

a)

b)

c)

d)

21.

Solve $\log_9\left(-3x-1\right)=\log_9\left(x^2-71\right)$

a)

$\left\{-8,4\right\}$

b)

$\left\{-10,7\right\}$

c)

No Solution

d)

$\left\{-10\right\}$

22.

Solve $\log_{20}\left(-5x+4\right)=\log_{20}\left(2x+8\right)$

a)

$\left\{-\frac{4}{7}\right\}$

b)

$\left\{-12\right\}$

c)

$\left\{10\right\}$

d)

$\left\{-4\right\}$

23.

Solve $\log_8\left(x^2-8\right)-\log_87=1$

a)

$\left\{2\right\}$

b)

No Solution

c)

$\left\{4,-4\right\}$

d)

$\left\{8,-8\right\}$

Unit 4 Test #3 Review (Activity 23 & 24)

Total questions: 23

Worksheet time: 12mins

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