Solve equations of the form aˣ = b for the variable x.
Equation Terms
Solution for x
3.0000
Solution (x)
The exponent required to reach the result from the given base.
Log₁₀(b)0.9031
ln(b)2.0794
About this calculator
Solving for Exponents
Exponential equations are equations where the variable appears in the exponent. To solve these, we typically use logarithms. If we have aˣ = b, we can take the logarithm of both sides to find x. This is the inverse operation of exponentiation.
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Pro Tips
The base 'a' must be positive and not equal to 1.
The result 'b' must be positive for a real solution to exist.
If you can write 'b' as a power of 'a', you can solve it without a calculator (e.g., 2ˣ = 8, so x = 3).
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Fun Facts
"Logarithms were invented by John Napier in 1614 to simplify astronomical calculations by turning multiplication into addition."
"The slide rule, used by engineers for centuries before electronic calculators, is essentially a physical implementation of logarithms."
"Benford's Law states that in many naturally occurring sets of numbers, the leading digit is likely to be small, which is explained by exponential distributions and logarithms."
