Logarithms and Logarithmic Functions: Algebra 2 Math Quiz – PDF Download
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.
🎯 Logarithms and Logarithmic Functions – Algebra 2 math quiz
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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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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: \(\log_{b} x=\frac{\ln x}{\ln b}\).
