# What is the inverse of y = a*ln(bx) ?

Mar 25, 2016

$y = \frac{{e}^{\frac{x}{a}}}{b}$

#### Explanation:

Write as $\frac{y}{a} = \ln \left(b x\right)$

Another way of writing the same thing is: ${e}^{\frac{y}{a}} = b x$

$\implies x = \frac{1}{b} \times {e}^{\frac{y}{a}}$

Where the is an $x$ write $y$ and where original $y$ was write $x$

$y = \frac{{e}^{\frac{x}{a}}}{b}$

This plot will be a reflection of the original equation about the plot of y=x.

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Read as $y$ equals $e$ raised to the power of $\frac{x}{a}$ all over $b$