Quiz about Unit 3 Exam Review

Question 1

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

Simplify: $$\log_216+\log_28$$

Accepted Answer

7

Answer

- 16

Answer

-2

Answer

8

Question 3

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)?

Accepted Answer

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

Answer

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

Answer

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

Answer

$$5e^x-18$$

Question 4

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 $$g\left(x\right)=\log_{ }\left(\frac{1}{2}x-4\right)+3$$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

How many solutions are there to the following logarithmic equation?

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

Accepted Answer

One Solution

Answer

No solution

Answer

Two solution

Answer

Three solution

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

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

Accepted Answer

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

Answer

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

Answer

$$4\ln x-8\ln y$$

Answer

$$4\ln x+8\ln y$$

Question 8

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 9

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?

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

Accepted Answer

17.357 years

Answer

17.672 years

Answer

18.245 years

Answer

18.123 years

Question 10

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?

Accepted Answer

2043

Answer

2040

Answer

2035

Answer

2025

Question 11

Determine each of the following exponential or logarithmic equations algebraically.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 12

Determine each of the following exponential or logarithmic equations algebraically.

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

Accepted Answer

x = ln 9

Answer

x=ln 2

Answer

x =ln 3

Answer

x = ln 6

Question 13

Determine each of the following exponential or logarithmic equations algebraically.

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

Accepted Answer

x = -27

Answer

x = -14

Answer

x = -8

Answer

x = -72

Unit 3 Exam Review

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