Can $x^2$ be expressed as an Exponential Function?
If we are looking at the graph of $x^2$ for $x>0$ is there some way to express this as an exponential function such as $a^{x+h}$. Is there infinetly many ways to express it as an exponential or no ways at all and how can we show this? Visually, to me it seemed that this was possible but I'm not sure on how to prove it.
Solution 1:
$x^2=|x|^2=\exp(2\ln(|x|)).$ Hence, your question is equivalent to asking if there exists some $A$ such that $Ax\equiv\ln(|x|).$ I think it is easy to see that this is not the case.