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

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

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

simplify

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

- lo g_{10} (x) - 1

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - (lo g_{10} (x) + lo g_{10} (10))

Apply log rule:

lo g_{a} (a) = 1

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

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