What is log_{3}(e)*ln(1/27) ?

The solution to log_{3}(e)*ln(1/27) is -3

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simplify log_{3}(e)*ln(1/27)

simplify

lo g_{3} (e) \cdot ln (\frac{1}{27})

- 3

Solution steps

lo g_{3} (e) ln (\frac{1}{27})

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

lo g_{3} (e) ln (\frac{1}{27}) = \frac{ln ( e )}{ln ( 3 )} \cdot \frac{ln ( \frac{1}{27} )}{ln ( e )}

= \frac{ln ( e )}{ln ( 3 )} \cdot \frac{ln ( \frac{1}{27} )}{ln ( e )}

Refine

= \frac{ln ( \frac{1}{27} )}{ln ( 3 )}

Simplify

ln (\frac{1}{27}) : - 3 ln (3)

= \frac{- 3 ln ( 3 )}{ln ( 3 )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3 ln ( 3 )}{ln ( 3 )}

Cancel the common factor:

ln (3)

= - 3

- 3 x + 3 x

\frac{9}{15} - \frac{- 7}{12}

(- 4)^{1}

f (n) = \frac{n + 6}{n ^{2} + 8 n + 12}

\frac{28}{52}