How do I draw a log log or semi log graph in a normal graph?

Question

Say I have a function $y=f(x)$. Now how can I change the function to $y=g(x)$ so that when $y=g(x)$ is plotted in a normal graph it looks like the semi log or log log graph of the old $y=f(x)$.

Answer 1

Instead of guessing a formula, try to derive one. Suppose that $y_0=f(x_0)$ for some points in the $(x,y)$-plane. Let $(r_0,s_0)$ be the corresponding points in the log-log or semilog planes. Then, there are formulas $r_0=h(x_0)$ and $s_0=k(y_0)$. So, then $k^{-1}(s_0)=f(h^{-1}(r_0))$ is your desired formula. You can then solve for $s_0$ to get $s=k(f(h^{-1}(r)))$ to construct your graph.

Answer 2

For a semi-log graph ( log in the $x$ axis and linear in the $y$ axis) replace $x$ with $10^x$, i,e,. plot $y=f(10^x)$. The $x$ value in the horizontal axis should correspond to $10^x$ in the semi-log graph (like $1, 2, 3, \cdots$ goes to $10, 100, 1000, \cdots$).

For the case of log in the $y$ axis and linear in the $x$ axis, keep $x$ as it is but instead of $y=f(x)$ plot $y=\log(f(x))$.

For log-log graph do both, and plot $y=\log(f(10^x))$.

Here $\log$ is 10-based.