log Log Calculator
Calculate logarithms with any base, or solve exponential equations of the form base^y = x.
Solve log_b(x)
Result
Logarithm Formulas
A logarithm answers the question: "to what power must the base be raised to produce this number?"
If log_b(x) = y, then b^y = x
Worked Example
The calculator loads in "log_b(x) = ?" mode with x = 1000 and base b = 10. Using the change-of-base formula, log₁₀(1000) = ln(1000) / ln(10) = 3, which checks out since 10³ = 1000. Switching to the "b^y = ?" tab with its own defaults (base 2, exponent 10) would instead compute 2¹⁰ = 1024.
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.