What is simplify-log_{10}((1.8*10^{-5})(0.1)) ?

The solution to simplify-log_{10}((1.8*10^{-5})(0.1)) is -log_{10}((1.8)/(100000))-log_{10}(0.1)

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simplify-log_{10}((1.8*10^{-5})(0.1))

simplify

- lo g_{10} ((1.8 \cdot 1 0^{- 5}) (0.1))

- lo g_{10} (\frac{1.8}{100000}) - lo g_{10} (0.1)

Decimal Notation

5.74472 \dots

Solution steps

- lo g_{10} ((1.8 \cdot 1 0^{- 5}) (0.1))

Apply log rule:

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

lo g_{10} ((1.8 \cdot 1 0^{- 5}) (0.1)) = lo g_{10} (1.8 \cdot 1 0^{- 5}) + lo g_{10} (0.1)

= - (lo g_{10} (0.1) + lo g_{10} (1 0^{- 5} \cdot 1.8))

lo g_{10} (1.8 \cdot 1 0^{- 5}) = lo g_{10} (\frac{1.8}{100000})

= - (lo g_{10} (0.1) + lo g_{10} (\frac{1.8}{100000}))

Distribute parentheses

= - (lo g_{10} (\frac{1.8}{100000})) - (lo g_{10} (0.1))

Apply minus-plus rules

+ (- a) = - a

= - lo g_{10} (\frac{1.8}{100000}) - lo g_{10} (0.1)

ln (\frac{439.7918}{1105.7918})

ln (\frac{0.9636}{1 - 0.9636})

ln (- \frac{3}{5} e^{- 5 t})

1 - 4 ln (\frac{5}{4})

lo g_{8} (w^{6} u)

What is simplify-log_{10}((1.8*10^{-5})(0.1)) ?
The solution to simplify-log_{10}((1.8*10^{-5})(0.1)) is -log_{10}((1.8)/(100000))-log_{10}(0.1)