Question

Find the inverse of y= e cubed root of x?

Answer 1

Would you not take ln of both sides?

Answer 2

yes, as the first step
what do you get ?

Answer 3

\[\ln y = x \sqrt[3]{x}\]

Answer 4

just
\[ \ln y = \sqrt[3]{x} \]

Answer 5

Oh yes, my bad. they cancel

Answer 6

now how do you undo the cubed root ?

Answer 7

Cube it!

Answer 8

fyi,
\[ \ln\left(e^{stuff}\right) = stuff \]

Answer 9

yes so cube both sides
use parens around ln y