Exponential equation solver
Enter the multiplier a, base b and result c to find x. Useful for growth, doubling and decay problems.
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How to use it
- Enter multiplier a, base b and result c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Divide by a to get bˣ = c/a, then take logs: x = ln(c/a) / ln(b). This needs b > 0, b ≠ 1 and c/a positive.
Example
Inputs: Multiplier a = 3, Base b = 2, Result c = 48. Result: Value of x: 4; Value of bˣ = c/a: 16; Check: a × bˣ: 48.
Limits and caveats
- Covers a × bˣ = c only; equations with more than one exponential term are not supported.
- The result is rounded to 8 decimal places.
Questions about this tool
How many years to double at 5% growth a year?
Enter a = 100, b = 1.05, c = 200. x is about 14.21 years.
Why is there no solution when c is negative and a positive?
A positive base to any power is always positive, so it can never equal a negative number.
Can I solve 2ˣ = 10?
Yes. Enter a = 1, b = 2, c = 10 to get x = ln(10)/ln(2), about 3.3219.