What is simplify-log_{10}(3*10^{-17}) ?

The solution to simplify-log_{10}(3*10^{-17}) is -log_{10}(3)+17

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simplify-log_{10}(3*10^{-17})

simplify

- lo g_{10} (3 \cdot 1 0^{- 17})

- lo g_{10} (3) + 17

Decimal Notation

16.52287 \dots

Solution steps

- lo g_{10} (3 \cdot 1 0^{- 17})

Apply log rule:

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

lo g_{10} (3 \cdot 1 0^{- 17}) = lo g_{10} (3) + lo g_{10} (1 0^{- 17})

= - (lo g_{10} (3) + lo g_{10} (1 0^{- 17}))

Apply log rule:

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

lo g_{10} (1 0^{- 17}) = - 17 lo g_{10} (10)

= - (lo g_{10} (3) - 17 lo g_{10} (10))

17 lo g_{10} (10) = 17

= - (lo g_{10} (3) - 17)

Distribute parentheses

= - (lo g_{10} (3)) - (- 17)

Apply minus-plus rules

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

= - lo g_{10} (3) + 17

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What is simplify-log_{10}(3*10^{-17}) ?
The solution to simplify-log_{10}(3*10^{-17}) is -log_{10}(3)+17