Algebra 2 Exponential Log Equations Quiz

Contents

This algebra 2 exponential log equations quiz asks 10 multiple-choice questions on solving exponential and logarithmic equations, and each answer comes with a short explanation.

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

Score: 0 / 10

Answered: 0 / 10

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.

A Only $x=-2$

B Both $x=4$ and $x=-2$

C No solution

D Only $x=4$

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?

A About 13.86 years

B About 14.21 years

C About 20.00 years

D About 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.

A 15 days

B 10 days

C 20 days

D 35 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

🎉 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 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.