Inverse function of y=10^x

Question

How do I find the inverse function of $y=f(x)=10^x$? As per my knowledge I have to swap $x$ for $y$. In that case it'll be $x=10^y$. Is that correct?

Answer 1

$$ f(x)=y=10^x $$

you are correct in finding the inverse of a function by swapping the variables, so

$$ \begin{align*} &f^{-1}(x) = x = 10^y \\ &f^{-1}(x) = y = \log_{10}(x) \quad (1) \end{align*}$$

where $ f^{-1}(x) $ is the inverse of $f(x)$

$(1)$ This step uses the property of logarithms that $x=b^y \implies y=\log_b(a)$