# Thread: exp(log(3))=3 or e^ln(3)=3, why?

1. ## exp(log(3))=3 or e^ln(3)=3, why?

exp(log(3))=3 or e^ln(3)=3, why?

I am reading an explanation like this:
"3 is the end result of growing instantly (using e) at a rate of ln(3). 3 = e^ln(3)"

BUT I cannot understand it... actually I don't understand so well, e as well ln ... please try to explain me while keeping this things in the mind - THANKS

2. From the definition of a logarithm: $y = log_a b \implies b = a^y$

When $a=b$ you get $y = log_a(a) \implies a = a^y \equiv a^1=a^y \equiv y=1$

Hence $log_a a =1$ and since $\ln(x) = \log_e(x)$ then $e^{\log_e(x)} = x$

==========================

Alternatively think of them as inverse operations which "cancel"