Solve exponential equation
Solve a·bˣ = c for x using logarithms.
Also known as: solve exponential equation calculator, exponential equation calculator, solve exponential equation, algebra math, algebra solve exponential equation
Inputs
Results update when you click Solve.
x
3.000000
2.0000·3.0000ˣ = 54.0000 → x = ln(27.0000) / ln(3.0000)
Steps
| Step | Detail |
|---|---|
| 1 | 3.0000ˣ = 27.0000 |
| 2 | x·ln(3.0000) = ln(27.0000) |
| 3 | x = 3.000000 |
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What this result means
Solve a·bˣ = c for x using logarithms. a·bˣ = c → bˣ = c/a → x = log_b(c/a) = ln(c/a) / ln(b).
Assumptions
- Rule dependency: Universal formula.
Method
a·bˣ = c → bˣ = c/a → x = log_b(c/a) = ln(c/a) / ln(b).
Example
2·3ˣ = 54 → 3ˣ = 27 → x = 3.
Frequently asked questions
Natural base e?+
Enter b ≈ 2.71828 for eˣ equations.