Question 1

Evaluate $$\sqrt{6 - 3.1}$$ and round your answer to three decimal places.

Accepted Answer

0.097

Question 2

Which of the following is the correct domain for the function $$f(x) = \ln(8 - 2x)$$?

Accepted Answer

$$(-\infty, 4)$$

Question 3

Given the function $$f(x) = 3e$$^{x+3}$$, which transformation has been applied to g(x) = e^x$ to obtain f(x$$)$$?

Accepted Answer

Horizontal shift left 3 units and vertical stretch by 3

Question 4

What is the accumulated value of a $7000 investment for 8 years at 3.75% interest compounded continuously? (Round to the nearest cent.)

Accepted Answer

$9449.01

Question 5

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

Accepted Answer

6

Question 6

Which of the following is the correct range for the function $$f(x) = 3 + e$$^{-x}$$?

Accepted Answer

$$(3, \infty)$$

Question 7

Expand the logarithmic expression $$\ln\left(\frac{x^3$ y^2$}{15z}\right) as $$much as possible.

Accepted Answer

$$3\ln x + 2\ln y - \ln 15 - \ln z$$

Question 8

Condense the expression $$\log_2$ 8 + \log_2$ y$$ into a single logarithm.

Accepted Answer

$$\log_2$(8y)$$

Question 9

Solve for $$x$$: $$3^{2x-9} = 27$

Accepted Answer

6

Question 10

Which of the following best describes the transformation from $$g(x) = \ln x to$$ $$f(x) = \ln(x-3) - 3$$?

Accepted Answer

Horizontal shift right 3 units, vertical shift down 3 units

Question 11

Evaluate $$\log_{10} 7000$$ using the change-of-base formula and round to four decimal places.

Accepted Answer

Question 12

Given the graph of $$f(x) = e^x$$, which of the following is the equation for the graph that passes through $$(0, 4)$$ and has a horizontal asymptote at $$y = 3$$?

Accepted Answer

Question 13

Solve for $$x in $$terms of natural logarithms: $$5^x = 27$$

Accepted Answer

$$x = \frac{\ln 27}{\ln 5}$$

Question 14

Which of the following is the correct domain for the function $$f(x) = \log_3$(x-2)$$?

Accepted Answer

$$(2, \infty)$$

Question 15

Expand $$\log_5$\left(\frac{x^4$}{y^5$}\right)$$ using properties of logarithms.

Accepted Answer

$$4\log_5$ x - 5\log_5$ y$$

Question 16

Solve for $$x$$: $$\log_5$(x-1) = 3$$

Accepted Answer

126

Question 17

Evaluate $$\ln(e$$^{15}$$)$$ without using a calculator.

Accepted Answer

15

Question 18

Which of the following is the correct range for the function $$f(x) = \log_3$(x-2)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 19

If $$f(x) = \ln(x-3) - 3$$, what is the vertical asymptote of $$f(x)$$?

Accepted Answer

$$x = 3$$

College Algebra Test Review: Exponential and Logarithmic Functions

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