E^-ln(x) = 1/x?

1. Sep 10, 2013

1s1

1. The problem statement, all variables and given/known data

Is $e^{-ln(x)}$ equal to $\frac{1}{x}$ ?

2. Relevant equations

3. The attempt at a solution

$e^{-ln(x)} = e^{ln(x^{-1})} = e^{ln(\frac{1}{x})} = \frac{1}{x}$ ?

Thanks!

2. Sep 10, 2013

Zondrina

Yes that is correct. It's a very common mistake that I see to not apply the log rules before eliminating $e$ and $ln$.