How do I rewrite a logarithm in exponential form, so as to plot it? $f(x) = 2\log x$

Question

How do I write $f(x)=2\log x$ in exponential form? Is $2(10)^y=x$ correct?

Answer 1

$y=2\mbox{log}x \ \Leftrightarrow \mbox{log}x=\frac{y}{2} \ \Leftrightarrow x=10^{\frac{y}{2}}.$

Answer 2

If we are given log(x), it is generally assumed that this is log base 10. We can re-write your problem as y=2 $log_{10}$(x), which is equivalent to $(1/2)y = log_{10}(x)$. Then we have $10^{y/2} = x$.

Answer 3

Here is the general case, \[ y=a\log_{b} x \] \[ \frac{y}{a}=\log_{b} x \] \[ b^{\frac{y}{a}}=b^{\log_{b} x}=x \] Usually \[ \log x=\log_{10} x \]

So if $a=2$ and $b=10$, then \[ x= 10^{\frac{y}{2}}=\sqrt{10^{y}} \]