Please solve with work and explain why and what you are doing
Write the Inverse of each function:
1) Y= log3X
2) Y= 2^(x/3)
$\displaystyle y=log_{3}(x)$
exchange the x and y and then solve for y
$\displaystyle x=log_{3}(y) \iff 3^x=y$
$\displaystyle f^{-1}(x)=3^x$
$\displaystyle y=2^{x/3}$ swapping the var
$\displaystyle x=2^{y/3} \iff log_{2}(x)=\frac{y}{3} \iff 3log_{2}(x)=y$
$\displaystyle f^{-1}(x)=3log_2(x)$
I don't understand 2 is a constant not a variable?
your equation is
$\displaystyle y=2^{\frac{x}{3}}$
The 2 is the base of eponential function.
if we interchange the variables we get
$\displaystyle x=2^{\frac{y}{3}}$ rewritting as a log we get
$\displaystyle log_{2}(x)=\frac{y}{3} \iff y= 3 log_{2}(x)$