Logarithmic functions > Logarithms
12345Logarithms

## Theory

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 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 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.