What is simplify-log_{10}(7.2*10^-14) ?

The solution to simplify-log_{10}(7.2*10^-14) is -log_{10}(7.2)+1-log_{10}(14)

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simplify-log_{10}(7.2*10^-14)

simplify

- lo g_{10} (7.2 \cdot 1 0^{-} 14)

- lo g_{10} (7.2) + 1 - lo g_{10} (14)

Decimal Notation

- 1.00346 \dots

Solution steps

- lo g_{10} (7.2 \cdot 1 0^{-} \cdot 14)

Apply log rule:

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

lo g_{10} (7.2 \cdot 1 0^{-} \cdot 14) = lo g_{10} (7.2) + lo g_{10} (1 0^{-}) + lo g_{10} (14)

= - (lo g_{10} (14) + lo g_{10} (7.2) + lo g_{10} (1 0^{-}))

Apply log rule:

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

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

= - (lo g_{10} (7.2) - lo g_{10} (10) + lo g_{10} (14))

Apply log rule:

lo g_{a} (a) = 1

= - (lo g_{10} (14) + lo g_{10} (7.2) - 1)

Distribute parentheses

= - (lo g_{10} (7.2)) - (- 1) - (lo g_{10} (14))

Apply minus-plus rules

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

= - lo g_{10} (7.2) + 1 - lo g_{10} (14)

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\frac{0.025693}{1} ln (\frac{1}{1.75 \cdot 1 0 ^{- 10}})

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What is simplify-log_{10}(7.2*10^-14) ?
The solution to simplify-log_{10}(7.2*10^-14) is -log_{10}(7.2)+1-log_{10}(14)