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Popular >

simplify log_{10}(1/(a^2))

Solution

simplify

lo g_{10} (\frac{1}{a ^{2}})

Solution

- 2 lo g_{10} (a)

Solution steps

lo g_{10} (\frac{1}{a ^{2}})

Simplify

\frac{1}{a ^{2}} : (a^{2})^{- 1}

= lo g_{10} ((a^{2})^{- 1})

Apply log rule

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

lo g_{10} ((a^{2})^{- 1}) = - 1 \cdot lo g_{10} (a^{2})

= - 1 \cdot lo g_{10} (a^{2})

Apply rule:

1 \cdot a = a

= - lo g_{10} (a^{2})

Apply log rule

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

- lo g_{10} (a^{2}) = - 2 lo g_{10} (a)

= - 2 lo g_{10} (a)

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Frequently Asked Questions (FAQ)

What is log_{10}(1/(a^2)) ?
The solution to log_{10}(1/(a^2)) is -2log_{10}(a)