What is simplify-log_{10}(1/x) ?

The solution to simplify-log_{10}(1/x) is log_{10}(x)

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simplify-log_{10}(1/x)

simplify

- lo g_{10} (\frac{1}{x})

lo g_{10} (x)

Solution steps

- lo g_{10} (\frac{1}{x})

Simplify

\frac{1}{x} : x^{- 1}

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

Apply log rule

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

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

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

Apply rule:

1 \cdot a = a

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

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

Apply rule:

- (- a) = a

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

= lo g_{10} (x)

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

lo g_{4} (3) + lo g_{4} (5)

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