What is simplify-log_{10}((10^{-14})/(1/30)) ?

The solution to simplify-log_{10}((10^{-14})/(1/30)) is 14-log_{10}(30)

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simplify-log_{10}((10^{-14})/(1/30))

simplify

- lo g_{10} (\frac{1 0 ^{- 14}}{\frac{1}{30}})

14 - lo g_{10} (30)

Decimal Notation

12.52287 \dots

Solution steps

- lo g_{10} (\frac{1 0 ^{- 14}}{\frac{1}{30}})

Apply log rule:

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

lo g_{10} (\frac{1 0 ^{- 14}}{\frac{1}{30}}) = lo g_{10} (1 0^{- 14}) - lo g_{10} (\frac{1}{30})

= - (lo g_{10} (1 0^{- 14}) - lo g_{10} (\frac{1}{30}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 14}) = - 14 lo g_{10} (10)

= - (- 14 lo g_{10} (10) - lo g_{10} (\frac{1}{30}))

14 lo g_{10} (10) = 14

= - (- lo g_{10} (\frac{1}{30}) - 14)

Apply log rule:

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

= - (- (- lo g_{10} (30)) - 14)

Apply rule

- (- a) = a

= - (- 14 + lo g_{10} (30))

Distribute parentheses

= - (- 14) - (lo g_{10} (30))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= 14 - lo g_{10} (30)

- lo g_{10} (\frac{5}{100})

lo g_{a} (3.15) + lo g_{a} (2.45)

\frac{1}{2} ln (1 + \frac{2 y}{x})

ln (\frac{- 130.42}{- 0.00222877})

ln (x (60 - y))

What is simplify-log_{10}((10^{-14})/(1/30)) ?
The solution to simplify-log_{10}((10^{-14})/(1/30)) is 14-log_{10}(30)