# How do you graph y=log_4(x+1)?

Nov 23, 2016

Change log base to $e$ and scale $y = \ln \left(x + 1\right)$ by $\frac{1}{\ln} 4$

#### Explanation:

$y = {\log}_{4} \left(x + 1\right)$

Remember that: ${\log}_{b} a = \ln \frac{a}{\ln} b$

Hence $y = \ln \frac{x + 1}{\ln} 4$

Therefore the graph of y will be the graph of $\ln \left(x + 1\right)$ scaled by $\frac{1}{\ln} 4$

$\ln \left(x + 1\right)$ is defined for $x > - 1$ and has a single zero at $x = 0$

The graph of $y$ is shown below:

graph{ln(x+1)/ln4 [-10, 10, -5, 5]}