But they give the same thing!

Calculus Level 3

True or false?

$\large e^{\ln x} = \ln \left( e^x \right)$

holds $\ \forall \ x \in \mathbb{R} \setminus \{0\}$ .

True False

2 solutions

Chew-Seong Cheong
May 28, 2017

When $x<0$ , $\ln x$ is complex then the LHS $e^{\ln x}$ is complex, while the RHS $\ln e^x = x$ , which is real. Therefore, $e^{\ln x} \ne \ln e^x$ for $x < 0$ .

Sahil Silare
May 31, 2017

Obviously false as domain of both the functions doesn't match.

But they give the same thing!

2 solutions

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