Practice Solving Exponential Equations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Solving exponential equations means finding the unknown variable trapped in an exponent by applying logarithms to both sides, using the power rule to bring the exponent down, and then isolating the variable with standard algebra.

When the variable is trapped in an exponent, logarithms free it. Taking log⁡\log of both sides brings the exponent down to ground level where you can solve for it using algebra.

Showing a random 20 of 50 problems.

Example 1

easy
Solve 8x=28^x = 2.

Example 2

easy
log⁡a(ax)=\log_a(a^x) = ___.

Example 3

medium
Solve 5x+2=3x−15^{x+2} = 3^{x-1}, exact form.

Example 4

medium
Solve 23x=52^{3x} = 5.

Example 5

medium
Solve ex+1=4e^{x+1} = 4.

Example 6

medium
Solve 2⋅5x=502\cdot 5^{x} = 50.

Example 7

easy
Solve 2x−1=162^{x-1} = 16 by matching bases.

Example 8

medium
A loan grows by A(t)=1000⋅1.05tA(t) = 1000\cdot 1.05^t. After how many full years does it first exceed $1500\$1500? Give exact tt.

Example 9

easy
Solve 2x=1162^x = \frac{1}{16}.

Example 10

challenge
Solve 32x−4⋅3x+3=03^{2x} - 4\cdot 3^x + 3 = 0.

Example 11

easy
Solve 32x=273^{2x} = 27.

Example 12

challenge
Find all real xx with 2x⋅5x=1042^x \cdot 5^x = 10^4.

Example 13

easy
Solve 4x=24^x = 2.

Example 14

easy
Solve 3x=813^x = 81.

Example 15

easy
Solve 3x=813^x = 81.

Example 16

hard
Solve 32x+1=5x3^{2x+1} = 5^{x}, exact form.

Example 17

challenge
Solve 4x−5⋅2x+4=04^x - 5\cdot 2^x + 4 = 0.

Example 18

medium
Solve 2x+3=7x−12^{x+3} = 7^{x-1}.

Example 19

easy
Solve 10x=100010^x = 1000.

Example 20

easy
To solve ax=ba^x = b for xx, apply ___ to both sides.
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