Solving Exponential and Logarithmic Equations: Algebra 2 Math Quiz – PDF Download
This 10-question multiple choice quiz checks solving exponential and logarithmic equations, extraneous solutions and applications to interest and half-life. Choose the one correct answer, then read each explanation.
Algebra 2Common Core: F-LE.A.4 · A-SSE.B.3c
🎯 Solving Exponential and Logarithmic Equations – Algebra 2 math quiz
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Question 1
Solve \(2^{x+1}=32\).
A\(x=5\)
B\(x=6\)
C\(x=16\)
D\(x=4\)
Question 2
The graph of \(y=3^{x}\) and the line \(y=50\) are shown. Solve \(3^{x}=50\) to the nearest thousandth.The curve crosses y = 50 between x = 3 and x = 4.
A\(x\approx 16.667\)
B\(x\approx 3.561\)
C\(x\approx 1.304\)
D\(x\approx 0.281\)
Question 3
Solve \(5\cdot 2^{x}=40\).
A\(x=8\)
B\(x=3\)
C\(x=4\)
D\(x\approx 5.13\)
Question 4
Solve \(\log_{3}(x-1)=2\).
A\(x=9\)
B\(x=7\)
C\(x=10\)
D\(x=5\)
Question 5
The graph of \(y=\log_{2} x+\log_{2}(x-2)\) is shown. Solve \(\log_{2} x+\log_{2}(x-2)=3\).The curve exists only for x > 2.
AOnly \(x=-2\)
BBoth \(x=4\) and \(x=-2\)
CNo solution
DOnly \(x=4\)
Question 6
Solve \(\ln x=3\). Round to the nearest hundredth.
A\(x\approx 8.15\)
B\(x\approx 1.10\)
C\(x\approx 20.09\)
D\(x\approx 9.00\)
Question 7
Ava invests \$1,000 at 5% interest compounded annually. After how many years does the balance first reach \$2,000?
AAbout 13.86 years
BAbout 14.21 years
CAbout 20.00 years
DAbout 28.41 years
Question 8
An 80 mg dose has half-life 5 days, as graphed. After how many days do 10 mg remain?The amount halves every 5 days.
A15 days
B10 days
C20 days
D35 days
Question 9
Rewrite \(3^{t}\) in the form \(e^{kt}\).
A\(e^{3t}\)
B\(e^{0.477t}\)
C\(e^{0.910t}\)
D\(e^{1.099t}\)
Question 10
Solve \(4^{x}-5\cdot 2^{x}+4=0\).
A\(x=0\) or \(x=2\)
B\(x=1\) or \(x=4\)
C\(x=0\) or \(x=4\)
D\(x=2\) only
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Remember:
Standards F-LE.A.4 and A-SSE.B.3c: solve \(ab^{ct}=d\) with logarithms and rewrite exponential expressions.
To solve \(b^{x}=k\), take logs: \(x=\frac{\ln k}{\ln b}\).
To solve \(\log_{b} x=c\), rewrite it as \(x=b^{c}\); then check that every log argument is positive.
Compound interest \(A=P(1+\frac{r}{n})^{nt}\), continuous growth \(A=Pe^{rt}\) and half-life \(N=N_{0}(\frac{1}{2})^{t/h}\) all reduce to exponential equations.
Rewrite \(b^{t}\) as \(e^{t\ln b}\) or \((b^{1/12})^{12t}\) to show a different growth rate.
