# How do you graph f(x)=log_3(x-1)?

Jun 12, 2018

See below

#### Explanation:

$f \left(x\right) = {\log}_{3} \left(x - 1\right)$

$= \ln \frac{x - 1}{\ln} 3$

Thus, $f \left(x\right)$ has the standard graph of $\ln x$ shifted 1 unit positive on the $x -$axis and scaled by $\frac{1}{\ln} 3$. Shown below.

Standard graph: $\ln x$
graph{ln(x) [-10, 10, -5, 5]}

Graph of $f \left(x\right)$
graph{ln(x-1)/ln3 [-10, 10, -5, 5]}