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How do you simplify $5 ln (\frac{1}{e^{2}})$ $5 ln (1/e^2)$ ?

1 Answer

Apr 20, 2016

$5 ln (\frac{1}{e^{2}}) = - 10$ $5ln(1/(e^2))=color(green)(-10)$

Explanation:

Remember: $ln a = k$ $ln a = k$ is equivalent to $e^{k} = a$ $e^k=a$

Considering $ln (\frac{1}{e^{2}}) = k$ $ln(1/(e^2))=k$
$XXX a = \frac{1}{e^{2}} = e^{- 2}$ $color(white)("XXX")a=1/(e^2)=e^(-2)$
so
$XXX k = - 2$ $color(white)("XXX")k=-2$

If $ln (\frac{1}{e^{2}}) = - 2$ $ln (1/(e^2))=-2$
then
$XXX 5 ln (\frac{1}{e^{2}}) = 5 \times (- 2) = - 10$ $color(white)("XXX")5ln(1/(e^2))=5xx(-2)=-10$

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