What is simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)}) ?

The solution to simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)}) is 14-log_{10}((10000)/(5.4))

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simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)})

simplify

- lo g_{10} (1 0^{- 14} \frac{1}{5.4 \cdot 1 0 ^{- 4}})

14 - lo g_{10} (\frac{10000}{5.4})

Decimal Notation

10.73239 \dots

Solution steps

- lo g_{10} (1 0^{- 14} \cdot \frac{1}{5.4 \cdot 1 0 ^{- 4}})

Apply log rule:

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

lo g_{10} (1 0^{- 14} \cdot \frac{1}{5.4 \cdot 1 0 ^{- 4}}) = lo g_{10} (1 0^{- 14}) + lo g_{10} (\frac{1}{5.4 \cdot 1 0 ^{- 4}})

= - (lo g_{10} (1 0^{- 14}) + lo g_{10} (\frac{1}{1 0 ^{- 4} \cdot 5.4}))

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}{5.4 \cdot 1 0 ^{- 4}}))

14 lo g_{10} (10) = 14

lo g_{10} (\frac{1}{5.4 \cdot 1 0 ^{- 4}}) = lo g_{10} (\frac{10000}{5.4})

= - (lo g_{10} (\frac{10000}{5.4}) - 14)

Distribute parentheses

= - (- 14) - (lo g_{10} (\frac{10000}{5.4}))

Apply minus-plus rules

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

= 14 - lo g_{10} (\frac{10000}{5.4})

ln (4 x^{6} y^{8})

- \frac{1}{π} ln (\frac{6}{2})

ln (\frac{3}{- 1})

0.15 \cdot lo g_{10} (1.31) + 0.65 \cdot lo g_{10} (\frac{45.57 + 176}{60})

lo g_{e} (\frac{x}{e})

What is simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)}) ?
The solution to simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)}) is 14-log_{10}((10000)/(5.4))