How do you graph y=5ln(3x)?

Aug 24, 2016

y is defined for $x > 0$; y has a zero at $x = \frac{1}{3}$;
$y \to - \infty$ as $x \to 0$ (See graphs below)

Explanation:

$y = 5 \ln \left(3 x\right)$

Since $\ln a$ is defined for $a > 0 \to y$ is defined for $3 x > 0$
Hence for $x > 0$

Since $\ln a = 0$ for $a = 1 \to y = 0$ for $3 x = 1$
Hence y has a zero at $x = \frac{1}{3}$

For the purposes of graphing function $y$ the $5$ has the effect of amplifying the magnitude of $\ln 3 x$ five times.

graph{5ln(3x) [-46.2, 46.2, -23.1, 23.15]}

In the region closer to $\left(\frac{1}{3} , 0\right)$

graph{5ln(3x) [-1.915, 1.927, -0.941, 0.983]}