Question 1

Solve for $x$: $3x + 2 = -2(x - 4)$.

Accepted Answer

$x = -4$

Question 2

Which of the following is the correct solution to $2^{x+2} = \left( \frac{1}{4} \right)^{x-5}$?

Accepted Answer

$x = 2$

Question 3

Given $3^{2x-1} = 27^{x+1}$, what is the value of $x$?

Accepted Answer

$x = 3$

Question 4

What is the $y$-intercept (key point) of the function $y = 3^{x-2} - 3$?

Accepted Answer

$(0, -1)$

Question 5

For the function $y = \left( \frac{1}{2} \right)^x + 4$, what is the horizontal asymptote?

Accepted Answer

$y = 4$

Question 6

Which transformation occurs to the graph of $y = 2^x$ to produce $y = 2^{x+3} - 5$?

Accepted Answer

Shift left 3 units and down 5 units

Question 7

Solve for $x$: $\log_3 \left( \frac{1}{27} \right) = x$.

Accepted Answer

$x = -3$

Question 8

If $\log_{10} x = -5$, what is the value of $x$?

Accepted Answer

$x = 0.00001$

Question 9

Solve for $x$: $x^{\frac{2}{3}} = 25$.

Accepted Answer

$x = 125$

Question 10

Which of the following is the solution to $(2x + 4)^{\frac{2}{3}} = 64$?

Accepted Answer

$x = 4$

Question 11

What is the value of $x$ in $x^{\frac{3}{2}} = 32$?

Accepted Answer

$x = 64$

Question 12

Which of the following best describes the domain of $y = 2^{x+3} - 5$?

Accepted Answer

$x \in \mathbb{R}$

Question 13

If $y = 3^{x-2} - 3$, what is the equation of the horizontal asymptote?

Accepted Answer

$y = -3$

Question 14

Which of the following is the correct solution to $\log_3 x = 1$?

Accepted Answer

$x = 3$

Question 15

If $y = \left( \frac{1}{2} \right)^x + 4$, what is the $y$-intercept?

Accepted Answer

$(0, 5)$

Exponential and Logarithmic Equations: Mini-Quiz Review

Study Guide - Practice Questions