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Exponential and logarithmic functions — ACT practice questions

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• 45 questions on the paper
• 42 practice questions in the app
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Practice 42 Exponential and logarithmic functions questions in the app

What this topic is

Exponential and logarithmic functions on the ACT Mathematics test cover growth models, equations with base e, and the algebra used to isolate an exponent.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

If $\log_4 64+\log_4 x=5$, what is the value of $x$?

A2✗ Not this oneB4✗ Not this oneC16✓ CorrectD64✗ Not this one

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Answer: C — 16

$\log_4 64=3$ because $4^3=64$. Then $\log_4 x=5-3=2$, so $x=4^2=16$.

Question 2Mid

The real solution of the equation $4e^{3x}=36$ is:

A$\dfrac{\ln 9}{3}$✓ CorrectB$\ln 9$✗ Not this oneC$3\ln 36$✗ Not this oneD$\dfrac{\ln 36}{4}$✗ Not this one

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Answer: A — $\dfrac{\ln 9}{3}$

Divide by 4: $e^{3x}=9$. Take ln: $3x=\ln 9$, so $x=\dfrac{\ln 9}{3}$.

Question 3Easier

A bacteria culture grows according to $N(t)=2.4e^{1.2t}$, where $t$ is time in hours. Which of the following numbers is closest to the value of $N(8)$?

A$1\times 10^{4}$✗ Not this oneB$4\times 10^{4}$✓ CorrectC$1\times 10^{5}$✗ Not this oneD$2\times 10^{5}$✗ Not this one

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Answer: B — $4\times 10^{4}$

$N(8)=2.4e^{9.6}$. Since $e^{9.6}\approx 14{,}740$, $2.4(14{,}740)\approx 35{,}376$, nearest $4\times 10^{4}$.

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