Logarithmic Function

L2MAEL

---

A logarithmic equation is basically the inverted function of a Exponential Function function; logarithmics are related to exponentials.

Equation of the function below: $y={\log }_{2}x$

the generic equation is:

$y={\log }_a(x-p)+q$

..where you can translate the graph by modifying the $p$ and $q$ coordinates.

By modifying the value of $p$, you can translate the graph along the $x$ axis,

..and by modifying the value of $q$, you can translate the graph along the $y$ axis.

$a$ again is the scale factor of the function, where if you increase it, the function turns into a more sleep slope.

However, $a$ cannot be lower or equal to 1, as it would make the graph linear, or undefined.

The asymptote of this function is the value of $p$.

(Asymptotes are explained in the Exponential Function page.)

If you have noticed from the two graphs from the exponential, and the logarithmic,

..these two graphs mirror each other. Equations are below:

$y=2^x$

$y={\log }_{2}x$

As mentioned twice, exponentials are related to logarithms, and using a table, you can see that the $x$ and $y$ pairs are inverted.