What is simplify-log_{10}((10^{-14})/(2*10^{-9)}) ?

The solution to simplify-log_{10}((10^{-14})/(2*10^{-9)}) is 14-log_{10}(500000000)

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simplify-log_{10}((10^{-14})/(2*10^{-9)})

simplify

- lo g_{10} (\frac{1 0 ^{- 14}}{2 \cdot 1 0 ^{- 9}})

14 - lo g_{10} (500000000)

Decimal Notation

5.30102 \dots

Solution steps

- lo g_{10} (\frac{1 0 ^{- 14}}{2 \cdot 1 0 ^{- 9}})

Apply log rule:

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

lo g_{10} (\frac{1 0 ^{- 14}}{2 \cdot 1 0 ^{- 9}}) = lo g_{10} (1 0^{- 14}) - lo g_{10} (2 \cdot 1 0^{- 9})

= - (lo g_{10} (1 0^{- 14}) - lo g_{10} (1 0^{- 9} \cdot 2))

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} (2 \cdot 1 0^{- 9}))

14 lo g_{10} (10) = 14

lo g_{10} (2 \cdot 1 0^{- 9}) = lo g_{10} (\frac{1}{500000000})

= - (- lo g_{10} (\frac{1}{500000000}) - 14)

Apply log rule:

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

= - (- (- lo g_{10} (500000000)) - 14)

Apply rule

- (- a) = a

= - (- 14 + lo g_{10} (500000000))

Distribute parentheses

= - (- 14) - (lo g_{10} (500000000))

Apply minus-plus rules

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

= 14 - lo g_{10} (500000000)

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

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What is simplify-log_{10}((10^{-14})/(2*10^{-9)}) ?
The solution to simplify-log_{10}((10^{-14})/(2*10^{-9)}) is 14-log_{10}(500000000)