Logarithm Calculator

Calculate natural logarithms (ln), common logarithms (log₁₀), and logarithms with custom bases. Perfect for solving exponential equations and working with logarithmic functions.

Number

Logarithm Formulas

Natural Log: ln(x) = log_e(x)

Common Log: log(x) = log₁₀(x)

Custom Base: log_b(x) = ln(x) / ln(b)

Key Properties:

• log_b(b) = 1

• log_b(1) = 0

• log_b(b^x) = x

• b^log_b(x) = x

Logarithm Rules

Product Rule: log(x×y) = log(x) + log(y)

Quotient Rule: log(x÷y) = log(x) - log(y)

Power Rule: log(xⁿ) = n×log(x)

Change of Base: log_a(x) = log_b(x) ÷ log_b(a)

Inverse: e^ln(x) = x

Common Applications

• Solving exponential equations

• Compound interest calculations

• Population growth models

• Earthquake magnitude (Richter scale)

• Sound intensity (decibels)

• pH calculations in chemistry

• Information theory (bits)