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Popular >

simplify log_{a}(1/(a^5))

Solution

simplify

lo g_{a} (\frac{1}{a ^{5}})

Solution

- 5

Solution steps

lo g_{a} (\frac{1}{a ^{5}})

Simplify

\frac{1}{a ^{5}} : (a^{5})^{- 1}

= lo g_{a} ((a^{5})^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{a} ((a^{5})^{- 1}) = - 1 \cdot lo g_{a} (a^{5})

= - 1 \cdot lo g_{a} (a^{5})

Apply rule:

1 \cdot a = a

= - lo g_{a} (a^{5})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{a} (a^{5}) = 5

= - 5

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Frequently Asked Questions (FAQ)

What is log_{a}(1/(a^5)) ?
The solution to log_{a}(1/(a^5)) is -5