Algebra
Change of base
Divides the natural log of the number by the natural log of the base. Any logarithm works in both places, so log(x) / log(b) gives the same answer.
The Formula
log_b(x) = ln(x) / ln(b)
Divides the natural log of the number by the natural log of the base. Any logarithm works in both places, so log(x) / log(b) gives the same answer.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| x | Argument | dimensionless | The number whose logarithm you want. |
| b | Base | dimensionless | The base of the logarithm you want. |
| ln | Natural logarithm | dimensionless | Logarithm to base e, available on any scientific calculator. |
What Each Symbol Means
xdimensionless
Argument
The number whose logarithm you want.
bdimensionless
Base
The base of the logarithm you want.
lndimensionless
Natural logarithm
Logarithm to base e, available on any scientific calculator.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a logarithm page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Logarithm, filed under Math. Every number the guide produces comes from substituting into this one line.