How is e^logx = x ? What's intuition behind this...I wonder

e^ln(x) = x

It's the same thing as:

2^log[2](x) = x
3^log[3](x) = x
10^log[10](x) = x

e^log[e](x) = e^ln(x) = x

[] denotes base.

Hello.

First, it should be noted that here, log x is the natural log of x (a lot of times it is written ln x to avoid confusion).

Second, e^x and ln x are inverse operations. In other words, they undo each other. It would be like if you added 5, and then subtracted 5 from an equation.

Hope this helps.

By definition, ln(a) is b such that e^b = a.
Substituting ln(a) for b, we have e^ln(a) = a.

I think you're thinking of e^lnx = x

or maybe even

10^logx = x
because :
e^logx is not = x