In mathematics|lang=en terms the difference between logarithm and exponent

is that logarithm is (mathematics) for a number $x$, the power to which a given base number must be raised in order to obtain $x$ written $\backslash log\_b\; x$ for example, $\backslash log\_\{10\}\; 1000\; =\; 3$ because $10^3\; =\; 1000$ and $\backslash log\_2\; 16\; =\; 4$ because $2^4\; =\; 16$ while exponent is (mathematics) the result of a logarithm, between a base and a power for example the $2$ in $\backslash log\_b(p)=2$.

As nouns the difference between logarithm and exponent

is that logarithm is (mathematics) for a number $x$, the power to which a given base number must be raised in order to obtain $x$ written $\backslash log\_b\; x$ for example, $\backslash log\_\{10\}\; 1000\; =\; 3$ because $10^3\; =\; 1000$ and $\backslash log\_2\; 16\; =\; 4$ because $2^4\; =\; 16$ while exponent is one who expounds, represents or advocates.