Question 1

Which of the following is the correct transformation for the graph of $$f(x) = \log(x-1) + 2$$ compared to $$f(x) = \log(x)$$?

Accepted Answer

Shift right by 1 unit and up by 2 units

Question 2

Given $$A = P(1 + \frac{r}{n}$$)^{nt}$$ and A$$ = $$Pe^{rt}$$, which investment yields a greater return over 4 years: $$8.25\%$$ compounded quarterly or $$8.25\%$$ compounded continuously, if you invest $$6000$$?

Accepted Answer

Continuous compounding yields a greater return

Question 3

Which of the following is the equivalent exponential form of $$5 = \log_5$ 32$$?

Accepted Answer

$$5^5 = 32$

Question 4

Evaluate $$\log_2$ 64$$ without a calculator.

Accepted Answer

$$x = 6$$

Question 5

Which of the following is the correct logarithmic form of $$7^y = 200$$?

Accepted Answer

$$\log_7$ 200 = y$$

Question 6

Expand $$\log(10,000x)$$ using properties of logarithms.

Accepted Answer

$$\log 10,000 + \log x$$

Question 7

Condense $$\log x + 2\log y - \log 7 - \log(x+1)^2$ into a single logarithm.

Accepted Answer

$$\log \left( \frac{xy^2$}{7(x+1)^2$} \right)$$

Question 8

Solve for $$x$$: $$32^x = 8$$

Accepted Answer

$$x = \frac{3}{5}$$

Question 9

If $$\log_3$ x = -2$$, what is the value of $$x$$?

Accepted Answer

$$x = \frac{1}{9}$$

Question 10

Which of the following is the correct solution for $$e^{2x} - 5e^x - 3 = 0$?

Accepted Answer

$$x = \ln(3)$$ and $$x = \ln(-1) (no $$real solution for $$x = \ln(-1))$$

Question 11

Evaluate $$\log_{19} 141$$ using the change-of-base formula.

Accepted Answer

$$\frac{\ln 141}{\ln 19}$$

Question 12

Which graph represents $$y = 2e$$^{-x}$$?

Accepted Answer

A decreasing exponential curve starting at $$y=2$$ when $$x=0$$

Question 13

If $$f(x) = \ln(x+1) + 2$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e -1$$

Question 14

Which of the following is the correct expansion for $$\log \left( \frac{w^2$x}{y^4$z^5$$} \right)$?

Accepted Answer

$$2\log w + \log x - 4\log y - 5\log z$$

Question 15

Solve for $$x$$: $$\log_{13} x = 1$$

Accepted Answer

$$x = 13$$

Question 16

Which of the following is the correct equivalent exponential form of $$b = \log_6$ 64$$?

Accepted Answer

$$6^b = 64$$

Question 17

If $$f(x) = \log(x-1)$$, what is the vertical asymptote of the graph?

Accepted Answer

$$x = 1$$

Question 18

Which of the following is the correct solution for $$\log_{19} x = 1$$?

Accepted Answer

$$x = 19$$

Question 19

Given the exponential function $$f(x) = 574(1.026)^x$$ modeling population growth, what does the base $$1.026$$ represent?

Accepted Answer

The annual growth rate factor

Question 20

If $$\log_5$ 125 = y$$, what is the value of $$y$$?

Accepted Answer

$$y = 3$$

Exponential and Logarithmic Functions: Graphs, Properties, and Applications

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