log Log Calculator

Calculate logarithms with any base, or solve exponential equations of the form base^y = x.

Solve log_b(x)

Result

log₁₀(1000)
3
10^3 = 1000
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Logarithm Formulas

A logarithm answers the question: "to what power must the base be raised to produce this number?"

log_b(x) = ln(x) / ln(b) (change of base formula)
If log_b(x) = y, then b^y = x

Frequently Asked Questions

What is the difference between log and ln?

"log" (or log₁₀) uses base 10, while "ln" (natural log) uses base e ≈ 2.71828. Both are logarithms, just with different bases.

Can the base or number be negative or zero?

No. Logarithms are only defined for positive numbers and positive bases (excluding a base of 1). The calculator will show a validation note for invalid inputs.

What does "b^y = x" mode do?

It solves the inverse problem: given a base and an exponent, it calculates the resulting value x, rather than solving for the exponent.

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