A logarithm gives the index of a power. $a^x=N\quad\Longleftrightarrow\quad\log_a N=x$ \(a0,\

Question

A logarithm gives the index of a power.

$a^x=N\quad\Longleftrightarrow\quad\log_a N=x$

$a>0,\ a\ne1,\ N>0$. Here $a$ is the base and $x$ is the index.

Common and natural logarithms

Common logarithm: $\lg x=\log_{10}x$.

Natural logarithm: $\ln x=\log_e x$, where $e\approx2.718$.

Real logarithms of zero or negative numbers are undefined.

Accepted Answer

$a^b=c\Longleftrightarrow b=\log_a c$

Logarithms I – Conversion between Logarithmic and Exponential Form