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Popular >

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

Solution

simplify

lo g_{10} (\frac{1}{1 0 ^{x}})

Solution

- x

Solution steps

lo g_{10} (\frac{1}{1 0 ^{x}})

Simplify

\frac{1}{1 0 ^{x}} : (1 0^{x})^{- 1}

= lo g_{10} ((1 0^{x})^{- 1})

Apply log rule

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

lo g_{10} ((1 0^{x})^{- 1}) = - 1 \cdot lo g_{10} (1 0^{x})

= - 1 \cdot lo g_{10} (1 0^{x})

Apply rule:

1 \cdot a = a

= - lo g_{10} (1 0^{x})

Apply log rule:

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

lo g_{10} (1 0^{x}) = x

= - x

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Frequently Asked Questions (FAQ)

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