What is the inverse of $y = a \cdot ln (b x)$ $y = a*ln(bx)$ ?

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Answer 1 · 2016-03-25T21:44:47

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

Write as $\frac{y}{a} = ln (b x)$ $y/a=ln(bx)$

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

$\Rightarrow x = \frac{1}{b} \times e^{\frac{y}{a}}$ $=>x=1/bxx e^(y/a)$

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

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

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

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

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