Algebra
Definition of a logarithm
The logarithm is the exponent. Reading the equation backwards is often the fastest way to evaluate a simple logarithm by hand.
The Formula
log_b(x) = y means b^y = x
The logarithm is the exponent. Reading the equation backwards is often the fastest way to evaluate a simple logarithm by hand.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| x | Argument | dimensionless | The positive number whose logarithm you want. |
| b | Base | dimensionless | A positive number other than 1. |
| y | Logarithm | dimensionless | The power the base must be raised to. |
What Each Symbol Means
xdimensionless
Argument
The positive number whose logarithm you want.
bdimensionless
Base
A positive number other than 1.
ydimensionless
Logarithm
The power the base must be raised to.
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.