Question 1Mid
If , what is the value of ?
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Answer: C — 16
because . Then , so .
Study on the flyACTMathematicsExponential and logarithmic functions
Mathematics
Exponential and logarithmic functions — ACT practice questions
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What this topic is
Logarithms undo exponents, and that relationship drives Exponential and logarithmic functions.
The statement log base 2 of 8 equals 3 says the same thing as 2 cubed equals 8. To solve an equation where the variable sits in an exponent, the usual steps are isolating the exponential term and then taking a logarithm of both sides; with base e, that means the natural log, written ln.
ACT Mathematics also gives growth models such as a starting amount times e raised to a rate times t, and asks for an approximate value at a certain time, so calculator skill matters. Choices are often close decimals.
Sample questions
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Question 2Mid
The real solution of the equation is:
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Answer: A —
Divide by 4: . Take ln: , so .
Question 3Easier
A bacteria culture grows according to , where is time in hours. Which of the following numbers is closest to the value of ?
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Answer: B —
. Since , , nearest .
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Practice 45 Exponential and logarithmic functions questions in the app
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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