Exponential and logarithmic functions — ACT practice questions

Exponential and logarithmic functions on the ACT Mathematics test cover growth models, equations with base e, and the algebra used to isolate an exponent. A student must solve exponential equations for a real x, evaluate a culture or population model at a given time, and pick the choice closest to that value. Items often ask for the value of x, the real solution of an equation, or the nearest number to a modeled quantity. Choices are five numerical options. Common traps include using the wrong logarithm, dropping a coefficient while isolating the exponent, and rounding too soon.

Section: Mathematics 45 questions on the paper
42 practice questions in the app

Sample questions

Question 1

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

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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 2

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

A $\dfrac{\ln 9}{3}$
B $\ln 9$
C $3\ln 36$
D $\dfrac{\ln 36}{4}$

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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 3

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 $1\times 10^{4}$
B $4\times 10^{4}$
C $1\times 10^{5}$
D $2\times 10^{5}$

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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 $4\times 10^{4}$ .

Practice 42 Exponential and logarithmic functions questions in the app

Exponential and logarithmic functions — ACT practice questions

Sample questions

More ACT topics

Mathematics