Algebra 2 Logarithms Quiz with Answers – Free PDF

Contents

This algebra 2 logarithms quiz asks 10 multiple-choice questions on logarithms and logarithmic functions, and each answer comes with a short explanation.

This 10-question multiple choice quiz checks the meaning of logarithms, their graphs, properties and inverses. Pick the one correct answer for each question, then read the explanation to learn from any miss.

Algebra 2Common Core: F-LE.A.4 · F-BF.B.4a · F-IF.C.7e

🎯 Logarithms and Logarithmic Functions – Algebra 2 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Evaluate \(\log_{3} 81\).

A \(27\)

B \(3\)

C \(4\)

D \(\frac{1}{4}\)

Question 2

The graph of \(y=\log_{b} x\) is shown and passes through \((9,2)\). What is \(b\)?

Graph of y = log_b x passing through (9, 2)

A \(9\)

B \(81\)

C \(4.5\)

D \(3\)

Question 3

Which equation is the logarithmic form of \(5^{-2}=\frac{1}{25}\)?

A \(\log_{25} 5=-2\)

B \(\log_{5}\frac{1}{25}=-2\)

C \(\log_{-2}\frac{1}{25}=5\)

D \(\log_{5}(-2)=\frac{1}{25}\)

Question 4

What is the domain of \(f(x)=\log_{4}(x-5)\)?

A \(x < 5\)

B \(x > -5\)

C \(x\ge 5\)

D \(x > 5\)

Question 5

Which expression equals \(\log_{2}(x^{3}y)\)?

A \(3\log_{2} x+\log_{2} y\)

B \(3\log_{2} x\cdot\log_{2} y\)

C \(\log_{2} 3x+\log_{2} y\)

D \(\left(\log_{2} x\right)^{3}+\log_{2} y\)

Question 6

Simplify \(\log 4+\log 25\).

A \(\log 29\)

B \(100\)

C \(4\)

D \(2\)

Question 7

The graph of \(f(x)=\log_{3}(x+2)\) is shown with points \((-1,0)\), \((1,1)\) and \((7,2)\). What is its vertical asymptote?

Graph with points (-1,0), (1,1), (7,2) and asymptote x = -2

A \(x=-2\)

B \(x=2\)

C \(x=0\)

D \(y=-2\)

Question 8

Use the change of base formula to find \(\log_{2} 12\) to the nearest thousandth.

A \(0.279\)

B \(3.585\)

C \(6.000\)

D \(2.485\)

Question 9

What is the inverse of \(f(x)=2^{x}+1\)?

A \(f^{-1}(x)=\log_{2} x-1\)

B \(f^{-1}(x)=\log_{2}(x-1)\)

C \(f^{-1}(x)=\log_{2}(x+1)\)

D \(f^{-1}(x)=\frac{1}{2^{x}+1}\)

Question 10

Lemon juice has \([H^{+}]=10^{-2}\) mol/L. What is its pH, using \(\text{pH}=-\log[H^{+}]\)?

pH scale marking lemon juice at 2

A \(-2\)

B \(12\)

C \(2\)

D \(0.01\)

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards F-LE.A.4, F-BF.B.4a and F-IF.C.7e: define logarithms, find inverses, and graph logarithmic functions.
\(\log_{b} x=y\) is equivalent to \(b^{y}=x\); \(\log x\) uses base 10 and \(\ln x\) uses base \(e\).
The graph of \(y=\log_{b} x\) has domain \(x > 0\), x-intercept \((1,0)\) and the y-axis as its vertical asymptote.
Product, quotient and power rules: \(\log_{b} MN=\log_{b} M+\log_{b} N\), \(\log_{b}\frac{M}{N}=\log_{b} M-\log_{b} N\), \(\log_{b} M^{p}=p\log_{b} M\).
Change of base: \(\log_{b} x=\frac{\ln x}{\ln b}\).