Question 1

Which of the following correctly applies the product rule for exponents to simplify $x^3 \cdot x^5$?

Accepted Answer

$x^{8}$

Question 2

Simplify the expression $\dfrac{6x^7 n^5}{3x^2 n^6}$.

Accepted Answer

$2x^5 n^{-1}$

Question 3

Which of the following is NOT a correct property of exponents?

Accepted Answer

$a^m + a^n = a^{m+n}$

Question 4

Write the exponential equation $5^x = 90$ in logarithmic form.

Accepted Answer

$\log_5 90 = x$

Question 5

Evaluate $\log_{2}(\dfrac{1}{8})$ without a calculator.

Accepted Answer

$-3$

Question 6

Which of the following is equivalent to $\sqrt[3]{x^5}$ written with rational exponents?

Accepted Answer

$x^{5/3}$

Question 7

If $\log_{b}(x) = 2$, what is $x$ in terms of $b$?

Accepted Answer

$x = b^2$

Question 8

Condense the expression $\log_5(x+4) + \log_5(2x+1)$ using properties of logarithms.

Accepted Answer

$\log_5((x+4)(2x+1))$

Question 9

Solve for $x$: $2^{x+2} = 100$.

Accepted Answer

$x = \log_2 25$

Question 10

Which of the following is the correct change of base formula for $\log_3 38$?

Accepted Answer

$\dfrac{\ln 38}{\ln 3}$

Question 11

A population triples every time period. If the initial population is 5,600, which equation models the population $y$ after $x$ time periods?

Accepted Answer

$y = 5600 \cdot 3^x$

Question 12

Which of the following is a common error involving exponents?

Accepted Answer

$(a+b)^n = a^n + b^n$

Question 13

If $\log_{10}(x) = 3$, what is the value of $x$?

Accepted Answer

$x = 1000$

Question 14

Simplify $e^{\ln(7)}$.

Accepted Answer

$7$

Question 15

A medication's concentration in the bloodstream decreases according to $y = 50 - 30 \log_2(x)$, where $x$ is the number of days after administration. After how many days will the concentration be 35 units? (Round to one decimal place.)

Accepted Answer

$x = 2^{1/3} \approx 1.3$ days

Question 16

Which of the following is the correct way to write $\log_{a}(M) + \log_{a}(N)$ as a single logarithm?

Accepted Answer

$\log_{a}(MN)$

Question 17

If $\ln(x) = 2$, what is the value of $x$?

Accepted Answer

$x = e^2$

Question 18

Which of the following is the correct exponential form of the logarithmic equation $\log_4(x-2) = 3$?

Accepted Answer

$x-2 = 4^3$

Question 19

A bank account grows according to $y = 45,000 \cdot 1.06^x$, where $x$ is the number of years. What is the growth factor per year?

Accepted Answer

$1.06$

College Algebra Chapter 2 Study Notes: Exponents, Logarithms, and Exponential Growth

Study Guide - Practice Questions

Study Guide - Flashcards