What is simplify-log_{10}((10^{-14})/(4.54*10^{-3)}) ?

The solution to simplify-log_{10}((10^{-14})/(4.54*10^{-3)}) is 14+log_{10}((4.54)/(1000))

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simplify-log_{10}((10^{-14})/(4.54*10^{-3)})

simplify

- lo g_{10} (\frac{1 0 ^{- 14}}{4.54 \cdot 1 0 ^{- 3}})

14 + lo g_{10} (\frac{4.54}{1000})

Decimal Notation

11.65705 \dots

Solution steps

- lo g_{10} (\frac{1 0 ^{- 14}}{4.54 \cdot 1 0 ^{- 3}})

Apply log rule:

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

lo g_{10} (\frac{1 0 ^{- 14}}{4.54 \cdot 1 0 ^{- 3}}) = lo g_{10} (1 0^{- 14}) - lo g_{10} (4.54 \cdot 1 0^{- 3})

= - (lo g_{10} (1 0^{- 14}) - lo g_{10} (1 0^{- 3} \cdot 4.54))

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} (4.54 \cdot 1 0^{- 3}))

14 lo g_{10} (10) = 14

= - (- lo g_{10} (1 0^{- 3} \cdot 4.54) - 14)

lo g_{10} (4.54 \cdot 1 0^{- 3}) = lo g_{10} (\frac{4.54}{1000})

= - (- lo g_{10} (\frac{4.54}{1000}) - 14)

Distribute parentheses

= - (- 14) - (- lo g_{10} (\frac{4.54}{1000}))

Apply minus-plus rules

- (- a) = a

= 14 + lo g_{10} (\frac{4.54}{1000})

ln (\frac{104}{114})

lo g_{10} (\frac{( y ^{5} )}{z ^{2} x ^{3}})

lo g_{a} (\frac{( a ^{4} ) b}{c ^{3}})

lo g_{10} (\frac{10}{1 + 4 e ^{- 0.8 x}})

ln (200 (\frac{12}{23})^{\frac{1}{3}})

What is simplify-log_{10}((10^{-14})/(4.54*10^{-3)}) ?
The solution to simplify-log_{10}((10^{-14})/(4.54*10^{-3)}) is 14+log_{10}((4.54)/(1000))