Exponential Equation Solver
How It Works
This exponential equation solver uses established formulas to provide accurate results.
The basic rule:
- base^x = result
- x = log(result) / log(base)
- Change of base: logₐ(b) = ln(b) / ln(a)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
How do I solve an exponential equation?
Take the logarithm of both sides. For base^x = result, x = log(result)/log(base). You can use any log base — natural log and common log both work due to the change of base formula.
What is the change of base formula?
logₐ(b) = log(b)/log(a) = ln(b)/ln(a). This lets you evaluate logarithms in any base using a calculator that only has log₁₀ or ln.
Why must the base be positive and not equal to 1?
If the base is negative, the function is not well-defined for all real exponents. If the base is 1, then 1^x = 1 for all x, so the equation either has all solutions or none — it cannot solve for a specific x.