AP®MathsCollege BoardPrecalculusExam QuestionsExponential & Logarithmic FunctionsExponential & Logarithmic Equations & Inequalities

Exponential & Logarithmic Equations & Inequalities (College Board AP® Precalculus): Exam Questions

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Exponential & Logarithmic Equations & Inequalities

1
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1 mark

The functions g is given by g open parentheses x close parentheses equals 2 log subscript 3 x.

Solve g open parentheses x close parentheses equals 4 for values of x in the domain of g.

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2
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2 marks

The function m is given by m open parentheses x close parentheses equals e to the power of 2 x end exponent minus e to the power of x minus 12. Find all input values in the domain of m that yield an output value of 0.

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3
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1 mark

The function g is given by space g open parentheses x close parentheses equals e to the power of open parentheses x plus 3 close parentheses end exponent.

Solve g open parentheses x close parentheses equals 10 for values of x in the domain of g.

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4
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1 mark

The function g is given by g open parentheses x close parentheses equals 2.916 times open parentheses 0.7 close parentheses to the power of x.

Find all values of x, as decimal approximations, for which g open parentheses x close parentheses equals 2, or indicate that there are no such values.

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5
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1 mark

The function space f is given by space f open parentheses x close parentheses equals log subscript 5 x.

Solve space f open parentheses x close parentheses equals 3 for values of x in the domain of space f.

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6
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1 mark

The function space f is given by space f open parentheses x close parentheses equals e to the power of x plus 1 end exponent.

Find an expression for space f to the power of negative 1 end exponent open parentheses x close parentheses. Show the work that leads to your answer.

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7
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1 mark

The function g is given by g open parentheses x close parentheses equals log subscript 2 open parentheses x plus 5 close parentheses.

Find an expression for g to the power of negative 1 end exponent open parentheses x close parentheses. Show the work that leads to your answer.

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8
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1 mark

The function g is given by g open parentheses x close parentheses equals ln open parentheses x squared minus 9 close parentheses.

Solve g open parentheses x close parentheses equals ln space 40 for values of x in the domain of g.

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9
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2 marks

The function m is given by m open parentheses x close parentheses equals fraction numerator e to the power of 4 x end exponent over denominator e to the power of 4 x end exponent minus 12 end fraction. Find all input values in the domain of m that yield an output value of 4.

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10
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1 mark

The function k is given by k open parentheses x close parentheses equals 6 e to the power of open parentheses 2 x close parentheses end exponent minus e

Solve k open parentheses x close parentheses equals 2 e for values of x in the domain of k.

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11
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2 marks

The number of visitors to a museum, in thousands, t years after it opened is modeled by the function V open parentheses t close parentheses equals a open parentheses 1.08 close parentheses to the power of t, where a is a constant. Two years after the museum opened, there were 46.656 thousand visitors.

Find the value of a. Then find the value of t, as a decimal approximation, for which V open parentheses t close parentheses equals 100.

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12
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2 marks

The concentration of a medication in a patient's bloodstream, in milligrams per liter, t hours after administration is modeled by the function C open parentheses t close parentheses equals 12 open parentheses 0.75 close parentheses to the power of t.

The medication is effective only when its concentration is at least 2 milligrams per liter. Determine all values of t, as decimal approximations, for which the medication is effective. Show the work that leads to your answer.

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13
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2 marks

The function g is given by g open parentheses x close parentheses equals log subscript 3 open parentheses x minus 4 close parentheses plus 2.

Find an expression for g to the power of negative 1 end exponent open parentheses x close parentheses, and state the domain of g to the power of negative 1 end exponent. Show the work that leads to your answer.

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14
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2 marks

The function space f is given by space f open parentheses x close parentheses equals 5 minus 2 times 3 to the power of x plus 1 end exponent.

Find an expression for space f to the power of negative 1 end exponent open parentheses x close parentheses, and state the domain of space f to the power of negative 1 end exponent. Show the work that leads to your answer.

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