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Popular >

simplify log_{10}(1/(x^n))

Solution

simplify

lo g_{10} (\frac{1}{x ^{n}})

Solution

- n lo g_{10} (x)

Solution steps

lo g_{10} (\frac{1}{x ^{n}})

Simplify

\frac{1}{x ^{n}} : (x^{n})^{- 1}

= lo g_{10} ((x^{n})^{- 1})

Apply log rule

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

lo g_{10} ((x^{n})^{- 1}) = - 1 \cdot lo g_{10} (x^{n})

= - 1 \cdot lo g_{10} (x^{n})

Apply rule:

1 \cdot a = a

= - lo g_{10} (x^{n})

Apply log rule

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

- lo g_{10} (x^{n}) = - n lo g_{10} (x)

= - n lo g_{10} (x)

Popular Examples

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2 lo g_{10} (x) + 5 lo g_{10} (x + 3)

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Frequently Asked Questions (FAQ)

What is log_{10}(1/(x^n)) ?
The solution to log_{10}(1/(x^n)) is -nlog_{10}(x)