Common log
log10(1000)=3 because 10³=1000.
Calculate common, natural, and arbitrary-base logarithms, evaluate antilogs, and solve simple logarithmic equations with clear change-of-base steps.
A logarithm answers the question: what exponent raises a base to a given value? The equation log_b(x)=y is equivalent to b^y=x.
Logarithms require a positive value and a positive base other than 1 when working with real numbers.
The same result can use common logs: log10(x)/log10(b).
log_b(x) = ln(x) / ln(b)An antilog reverses a logarithm.
x = b^yValid when x>0, y≠0, and the resulting base is positive and not 1.
b = x^(1/y)log10(1000)=3 because 10³=1000.
ln(e)=1 because e¹=e.
log₂(32)=5 and log₅(125)=3.
log₂(x)=5 becomes x=2⁵=32.
The base-10 antilog of 3 is 10³=1000.
log_b(xy)=log_b(x)+log_b(y).
log_b(x/y)=log_b(x)−log_b(y).
log_b(x^k)=k log_b(x).
The common logarithm uses base 10. The natural logarithm, written ln, uses Euler's number e as its base.
Real logarithm inputs must be positive, and bases must be positive and not 1. Inverse calculations reuse the Exponent Calculator limits and reject non-finite overflow rather than showing Infinity.
It is the exponent required to raise a base to a specified positive value.
It is a logarithm with base 10.
It is a logarithm with base e, written ln.
Real logarithms are not defined for zero or negative values.
One raised to any exponent remains one, so it cannot provide a unique logarithm.
It reverses a logarithm by raising the base to the logarithm result.
It calculates any valid logarithm using a ratio of natural or common logarithms.
Yes, for log_b(x)=y when the inputs produce a valid positive base other than 1.