What are the parts of a logarithm called? $$\log_x y = z$$
$x$ is the base.
$z$ is the exponent or power.
What's $y$ called?

In the days when people used logithm tables, the integer part was the characteristic, and the decimal was the mantissa.
So $\log 20 = 1.30103$, makes 1 the characteristic (the bit after E...)and 0.30103 the mantissa (which the log tables tell you).
In $b^n = x$ or $\operatorname{lg}_b x = n$, b is the base, and n is the exponent, x is the argument of the function.
