Take a look at the applet: Logarithm
The solution of the equation
${g}^{x}=a$ is called the logarithm of
$a$ to base
$g$.
Notation:
$x={}^{g}log\left(a\right)$.
Since this equation only has solutions if
$0<g<1$ or
$g>1$ and if
$a>0$,
${}^{g}log\left(a\right)$ can only exist under these conditions.
For the time being you mostly use the intersect function of your graphing calculator
to determine
$x={}^{g}log\left(a\right)$.
The general definition for logarithms is:
from ${g}^{x}=y$ follows $x={}^{g}log\left(y\right)$;
from $x={}^{g}log\left(y\right)$ follows ${g}^{x}=y$;
The expressions
$x={}^{g}log\left(y\right)$ en
${g}^{x}=y$ are completely equivalent if
$0<g<1$ or
$g>1$ and if
$y>0$.
The exponential function and the logarithm with the same base are called inverse operations, since they reverse the effect of each other.