Precalculus Exponential and Logarithmic Equations Worksheet (PDF)

Precalculus math worksheet: Exponential and Logarithmic Equations – Maths PDF

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This exp log equations worksheet for Precalculus covers exponential and logarithmic equations (Common Core F-LE.A.4, F-BF.B.5, A-REI.D.11), with a free PDF to print.

These 20 problems practice exponential and logarithmic equations (Common Core F-LE.A.4, F-BF.B.5 and A-REI.D.11). You will match bases, use logarithms, solve log equations, check for extraneous solutions and solve growth and decay applications.

Precalculus · Common Core State Standards: F-LE.A.4, F-BF.B.5, A-REI.D.11

Exp log equations worksheet: exercises 1 to 10

Exercise 1 – Same base

Solve $2^{x}=64$.

Exercise 2 – Same base with a shift

Solve $5^{x-1}=125$.

Exercise 3 – Rewrite the base

Solve $9^{x}=27$.

Exercise 4 – Take a log

Solve $3^{x}=20$ to three decimal places.

Exercise 5 – Isolate first

Solve $4\cdot3^{x}=100$ to three decimal places.

Exercise 6 – Base e

Solve $e^{2x}=15$ to three decimal places.

Exercise 7 – Base e with isolation

Solve $2e^{3x}-1=9$ to three decimal places.

Exercise 8 – Simple log equation

Solve $\log_{2}(x+3)=4$.

Exercise 9 – Natural log equation

Solve $\ln(x-1)=3$ to the nearest hundredth.

Exercise 10 – Combine logs

Graph of y = log x + log(x – 3).

Solve $\log x+\log(x-3)=1$. Check for extraneous solutions.

Exercises 11 and up

Exercise 11 – Combine base-2 logs

Solve $\log_{2}x+\log_{2}(x-2)=3$.

Exercise 12 – Difference of logs

Solve $\log_{2}(x+6)-\log_{2}(x-1)=3$.

Exercise 13 – Solve by graphing

Graph of y = 2^x and y = 10.

Use the graph to estimate the solution of $2^{x}=10$, then compute it exactly with logarithms.

Exercise 14 – Savings goal

Mei invests $\$4{,}000$ at $5\%$ compounded yearly. How long until it reaches $\$6{,}000$? Give the answer to the nearest hundredth of a year.

Exercise 15 – Doubling time

Balance of a continuously compounded account.

Money grows by $A=Pe^{0.06t}$. Find the doubling time to the nearest hundredth of a year.

Exercise 16 – Half-life

Decay of a 200 g sample.

A $200$ g sample decays by $A(t)=200\left(\frac12\right)^{t/12}$ with $t$ in days. Find when $50$ g remain and when $30$ g remain (to the nearest hundredth).

Exercise 17 – Population growth

Population of a colony.

A colony has $P(t)=500e^{0.04t}$ members after $t$ years. When does it reach $1{,}500$?

Exercise 18 – Hydrogen concentration

Find $[\text{H}^{+}]$ for a solution with pH $5.3$, using $\text{pH}=-\log[\text{H}^{+}]$.

Exercise 19 – Sound intensity

A sound has level $85$ dB, where $L=10\log\frac{I}{I_{0}}$. Find $\frac{I}{I_{0}}$ to three significant figures.

Exercise 20 – Different bases

Solve $2^{x+1}=3^{x}$ to three decimal places.

Key facts behind this exp log equations worksheet

Key facts

Same base: if b^m = b^n then m = n.
Different bases: take ln of both sides, then x ln b = ln c.
log_b u = c is equivalent to u = b^c.
Check log solutions: arguments must be positive; reject extraneous values.
Continuous doubling time is ln 2 divided by the rate r.

How to use this exp log equations worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

All Precalculus chapters: Precalculus math.

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