Exponential Equations
A free Algebra II lesson from the “Exponential Models” unit, with a worked example and practice problems including step-by-step solutions.
Some exponential equations can be solved by rewriting both sides with the same base. Others need logarithms to undo the exponential expression.
What you'll learn
- Solve equations with common bases
- Use logarithms as inverse operations
- Check exponential solutions
Worked example
Problem. Solve 2^x = 32.
- Rewrite 32 as 2^5.
- 2^x = 2^5.
- So x = 5.
Answer: 5
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Solve 3^x = 81.
Show solution
- 81 = 3^4.
Answer: 4
2. Solve 5^x = 125.
Show solution
- 125 = 5^3.
Answer: 3
3. Solve 2^(x + 1) = 16.
Show solution
- 16 = 2^4, so x + 1 = 4.
Answer: 3
4. To solve 7^x = 20 exactly, you would use...
Choices: Logarithms · Factoring only · Completing the square · Triangle similarity
Show solution
- Logs undo exponentials.
Answer: Logarithms
5. A value grows by 6%. What multiplier is used each period?
Show solution
- Growth uses 1 plus the rate.
- 6% is 0.06.
- The multiplier is 1.06.
Answer: 1.06
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