Quiz about 6.5-6.7 Review

Question 1

Condense $$\log_bm+\log_bn$$

Accepted Answer

$$\log_b\left(mn\right)$$

Answer

$$\log_b\left(m+n\right)$$

Answer

$$\log_b\left(m-n\right)$$

Answer

$$\log_b\left(\frac{m}{n}\right)$$

Question 2

Condense $$\log_bm-\log_bn$$

Accepted Answer

$$\log_b\left(\frac{m}{n}\right)$$

Answer

$$\log_b\left(mn\right)$$

Answer

$$\log_b\left(m+n\right)$$

Answer

$$\log_b\left(m-n\right)$$

Question 3

Expand $$\log_b\left(mn\right)$$

Accepted Answer

$$\log_bm+\log_bn$$

Answer

$$\log_bm\cdot\log_bn$$

Answer

$$\frac{\log_bm}{\log_bn}$$

Answer

$$\log_bm-\log_bn$$

Question 4

Expand $$\log_b\left(\frac{m}{n}\right)$$

Accepted Answer

$$\log_bm-\log_bn$$

Answer

$$\log_bm\cdot\log_bn$$

Answer

$$\log_bm+\log_bn$$

Answer

$$\frac{\log_bm}{\log_bn}$$

Question 5

Simplify $$\log_bm^x$$

Accepted Answer

$$x\cdot\log_bm$$

Answer

$$x\div\log_bm$$

Answer

$$x+\log_bm$$

Answer

$$x-\log_bm$$

Question 6

Condense $$\log_218-\log_23$$

Accepted Answer

$$\log_26$$

Answer

$$\log_254$$

Answer

$$\log_221$$

Answer

$$\log_215$$

Question 7

Condense $$\log_24+\log_23$$

Accepted Answer

$$\log_212$$

Answer

$$\log_27$$

Answer

$$\log_21$$

Answer

$$\log_2\frac{4}{3}$$

Question 8

Expand $$\log\sqrt[3]{x}$$

Accepted Answer

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

Answer

$$3\log x$$

Answer

$$x\log3$$

Answer

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

Question 9

Use the change of base formula to simplify $$\log_73$$

Accepted Answer

0.565

Answer

-0.368

Answer

1.771

Answer

0.368

Question 10

Use the change of base formula to simplify $$\log_{25}83$$

Accepted Answer

1.373

Answer

0.521

Answer

0.728

Answer

-0.521

Question 11

Solve $$3^x=10$$

Accepted Answer

2.096

Answer

-0.523

Answer

0.477

Answer

0.523

Question 12

Solve $$32^{x-1}=\left(\frac{1}{2}\right)^{2-3x}$$

Accepted Answer

$$\frac{3}{2}$$

Answer

$$-\frac{1}{2}$$

Answer

$$-\frac{1}{8}$$

Answer

$$\frac{9}{14}$$

Question 13

Solve $$\log_8\left(3x-1\right)=\log_8\left(2x+9\right)$$

Accepted Answer

$$10$$

Answer

$$\frac{1}{10}$$

Answer

$$\frac{1}{2}$$

Answer

$$2$$

Question 14

Solve $$\ln\left(4-4n\right)=\ln\left(4-n\right)$$

Accepted Answer

$$0$$

Answer

$$-\frac{3}{8}$$

Answer

$$-\frac{8}{3}$$

Answer

$$3$$

Question 15

Solve $$\ln x+\ln\left(x+28\right)=\ln29$$

Accepted Answer

1

Answer

-29 and 1

Answer

29 and -1

Answer

29

Question 16

Solve $$\ln5x+\ln8=3$$

Accepted Answer

$$\frac{e^3}{40}$$

Answer

$$\frac{3e}{40}$$

Answer

$$\frac{3e-8}{5}$$

Answer

$$\frac{e^3-8}{5}$$

Question 17

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

Accepted Answer

$$\frac{10}{9}$$

Answer

No Solution

Answer

$$1$$

Answer

$$\frac{11}{2}$$

Question 18

What value(s) are not in the domain of $$y=\log x$$ ?

Accepted Answer

Zero and negative numbers

Answer

Zero and positive numbers

Answer

Negative numbers

Answer

Positive numbers

Question 19

The answer to a logarithmic equation can never be negative.

Accepted Answer

False

Answer

True

Question 20

Set up the change of base formula for $$\log_ma$$

Accepted Answer

$$\frac{\log a}{\log m}$$

Answer

$$\log\left(\frac{m}{a}\right)$$

Answer

$$\log\left(\frac{a}{m}\right)$$

Answer

$$\frac{\log m}{\log a}$$

Question 21

Solve $$8^{-3n}=\left(\frac{1}{16}\right)^{n-3}$$

Accepted Answer

$$-\frac{12}{5}$$

Answer

$$\frac{3}{2}$$

Answer

$$-6$$

Answer

$$\frac{3}{5}$$

Question 22

Solve $$\log x+5>13$$

Accepted Answer

$$x>10^8$$

Answer

$$x>80$$

Answer

$$x>8$$

Answer

$$x>\log8$$

Question 23

Solve $$\log x-2<1$$

Accepted Answer

$$0<x<1000$$

Answer

$$0<x<30$$

Answer

$$x<30$$

Answer

$$x<1000$$

Question 24

You deposit $5000 into an investment account that earns 3% annual interest. With interest compounded monthly, how long will it take to double your money?

Accepted Answer

23.1 years

Answer

2.3 years

Answer

5.4 years

Answer

53.7 years

Question 25

You bought a car for $15,000. After 6 years, its value was estimated to be $7000. Find the annual rate of depreciation.

Accepted Answer

11.9%

Answer

90.8%

Answer

13.5%

Answer

77.6%

Question 26

Find the equation of the exponential function that passes through the points (1,2) and (3,8).

Accepted Answer

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

Answer

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

Answer

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

Answer

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

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