Question

find the inverse of $y = 0.3^x$.
$y = \square$

Explanation:

Step1: Swap x and y variables

$x = 0.3^y$

Step2: Take log of both sides

$\log(x) = \log(0.3^y)$

Step3: Apply log power rule

$\log(x) = y\log(0.3)$

Step4: Solve for y

$y = \frac{\log(x)}{\log(0.3)}$

Step5: Rewrite as log base 0.3

$y = \log_{0.3}(x)$

Answer:

$\log_{0.3}(x)$ (or equivalently $\frac{\log(x)}{\log(0.3)}$)