How do you evaluate $e^{ln y}$ $e^(lny)$ ?

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How do you evaluate $e^{ln y}$ $e^(lny)$ ?

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Answer 1 · 2016-12-16T09:18:28

This expression evaluates ro $y$ $y$ for every positive real number $y$ $y$ . See explanation.

Explanation:

$f (y) = e^{y}$ $f(y)=e^y$ and $g (y) = ln y$ $g(y)=lny$ are inverse functions, so both compositions: $e^{ln y}$ $e^lny$ and ${ln e}^{y}$ $lne^y$ evaluate to $y$ $y$ in all their domains.

Since $ln y$ $lny$ is only defined for $y > 0$ $y>0$ the domain of the givenexpression is also $y > 0$ $y>0$ .

So the expression $e^{ln y}$ $e^lny$ is equal to $y$ $y$ for all positive real numbers $y$ $y$

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How do you evaluate $e^{ln y}$ $e^(lny)$ ?

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