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📉 Logarithm Calculator

📉 Logarithm Calculator

Evaluate logarithms in any base, convert between bases, and solve for an unknown exponent. Shows the change-of-base working so you can follow it on paper.

Quick base:
Enter a value and a base.
Rules and identities

logb(x) answers "b to what power gives x?", so it is only defined for x > 0 and b > 0, b \u2260 1. Change of base: logb(x) = ln(x) / ln(b). Product: log(xy) = log x + log y. Quotient: log(x/y) = log x \u2212 log y. Power: log(x\u207f) = n\u00b7log x. Doubling time at growth rate r is ln(2)/ln(1+r), which is what the Rule of 72 approximates.

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