Question 1

Which of the following is the correct domain for the function $$y = \log_{3}(x-1)$$?

Accepted Answer

$$x \u003e 1$$

Question 2

Given the exponential function $$y = 2$$^{x-2}$$ + 1$$, what is the horizontal asymptote?

Accepted Answer

$$y = 1$$

Question 3

If $$y = \log_{2}(x+3) - 2$$, which transformation is applied to the parent function $$y = \log$$_{2}$$x$$?

Accepted Answer

Shift left 3 units and down 2 units

Question 4

What is the solution to $$\log$$_{4}$$x = 2$$?

Accepted Answer

$$x = 16$$

Question 5

Which of the following is the range of the function $$y = 3$$^{x}$$ - 1$$?

Accepted Answer

$$(-1, \infty)$$

Question 6

Rewrite the equation $$5^{x} = 25$ in logarithmic form.

Accepted Answer

$$\log$$_{5}$$25 = x$$

Question 7

Evaluate $$\log$$_{2}$$64.$$

Accepted Answer

$$6$$

Question 8

Which of the following best describes the transformation for $$y = -\frac{1}{2}2$$^{x}$$ + 1$$ compared to $$y = 2$$^{x}$$?

Accepted Answer

Reflected over x-axis, vertically compressed by $$\frac{1}{2}$$, shifted up 1

Question 9

Solve for $$x$$: $$\log_{3}(x^2$) = 4.$$

Accepted Answer

$$x = 9 or$$ $$x = -9$$

Question 10

Which of the following is the correct expanded form of $$\log_{3}\left(\frac{a^4$b^5$$}{$$c^2$$}\right)$?

Accepted Answer

$$4\log$$_{3}$$a + 5\log$$_{3}$$b - 2\log$$_{3}$$c$$

Question 11

A radioactive isotope decays according to $$y = 521(0.63)^t. $$What is the amount after 3 years?

Accepted Answer

$$y \approx 130$$

Question 12

Which of the following is the correct change of base formula for $$\log$$_{b}$$a$$?

Accepted Answer

$$\frac{\log$$_{k}$$a}{\log$$_{k}$$b}$$

Question 13

If $$y = \log_{2}(x-5) + 1$$, what is the y-intercept?

Accepted Answer

There is no y-intercept

Question 14

Solve for $$x$$: $$2^{x-1} = 16$.

Accepted Answer

$$x = 5$$

Question 15

Which of the following is the correct logarithmic form of $$9^{\frac{1}$${2}} = 3$$?

Accepted Answer

$$\log$$_{9}$$3 = \frac{1}{2}$$

Question 16

A savings account balance is modeled by $$y = 1172.2(1.02)^t. $$What is the balance after 8 years?

Accepted Answer

$$y \approx 1360$$

Question 17

Which of the following is the correct condensed form of $$2\log$$_{3}$$x + \log$$_{3}$$y$$?

Accepted Answer

$$\log_{3}(x^2$y)$$

Question 18

Given $$y = \log_{2}(x-3)$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 19

Evaluate $$\log$$_{5}$$125.$$

Accepted Answer

$$3$$

Exponential and Logarithmic Functions: Graphs, Properties, and Applications

Study Guide - Practice Questions