What is simplify-log_{10}(3.98(10^{-8})) ?

The solution to simplify-log_{10}(3.98(10^{-8})) is -log_{10}(3.98)+8

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simplify-log_{10}(3.98(10^{-8}))

simplify

- lo g_{10} (3.98 (1 0^{- 8}))

- lo g_{10} (3.98) + 8

Decimal Notation

7.40011 \dots

Solution steps

- lo g_{10} (3.98 (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (3.98 (1 0^{- 8})) = lo g_{10} (3.98) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (3.98) + lo g_{10} (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (1 0^{- 8}) = - 8 lo g_{10} (10)

= - (lo g_{10} (3.98) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (3.98) - 8)

Distribute parentheses

= - (lo g_{10} (3.98)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (3.98) + 8

ln (\frac{5}{4 m ^{8}})

ln (\frac{54000}{50000})

ln (w x yz)

ln (\frac{- 1}{x ^{2}} e^{x})

lo g_{10} ((1 - i)^{4})

What is simplify-log_{10}(3.98(10^{-8})) ?
The solution to simplify-log_{10}(3.98(10^{-8})) is -log_{10}(3.98)+8