What is log^{-1}_{10}((0.1)/(20))-1 ?

The solution to log^{-1}_{10}((0.1)/(20))-1 is -1/(log_{10)(200)}-1

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simplify log^{-1}_{10}((0.1)/(20))-1

simplify

lo g_{10}^{- 1} (\frac{0.1}{20}) - 1

- \frac{1}{lo g _{10} ( 200 )} - 1

Decimal Notation

- 1.43458 \dots

Solution steps

lo g_{10} (\frac{0.1}{20})^{- 1} - 1

Apply exponent rule:

a^{- 1} = \frac{1}{a}

lo g_{10} (\frac{0.1}{20})^{- 1} = \frac{1}{lo g _{10} ( \frac{0.1}{20} )}

= \frac{1}{lo g _{10} ( \frac{0.1}{20} )} - 1

lo g_{10} (\frac{0.1}{20}) = - lo g_{10} (200)

= \frac{1}{- lo g _{10} ( 200 )} - 1

Apply the fraction rule:

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

\frac{1}{- lo g _{10} ( 200 )} = - \frac{1}{lo g _{10} ( 200 )}

= - \frac{1}{lo g _{10} ( 200 )} - 1

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What is log^{-1}_{10}((0.1)/(20))-1 ?
The solution to log^{-1}_{10}((0.1)/(20))-1 is -1/(log_{10)(200)}-1