What is simplify-log_{10}(9*10^{-12}) ?

The solution to simplify-log_{10}(9*10^{-12}) is -2log_{10}(3)+12

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simplify-log_{10}(9*10^{-12})

simplify

- lo g_{10} (9 \cdot 1 0^{- 12})

- 2 lo g_{10} (3) + 12

Decimal Notation

11.04575 \dots

Solution steps

- lo g_{10} (9 \cdot 1 0^{- 12})

Apply log rule:

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

lo g_{10} (9 \cdot 1 0^{- 12}) = lo g_{10} (9) + lo g_{10} (1 0^{- 12})

= - (lo g_{10} (9) + lo g_{10} (1 0^{- 12}))

Apply log rule:

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

lo g_{10} (1 0^{- 12}) = - 12 lo g_{10} (10)

= - (lo g_{10} (9) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (9) - 12)

lo g_{10} (9) = 2 lo g_{10} (3)

= - (2 lo g_{10} (3) - 12)

Distribute parentheses

= - (2 lo g_{10} (3)) - (- 12)

Apply minus-plus rules

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

= - 2 lo g_{10} (3) + 12

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What is simplify-log_{10}(9*10^{-12}) ?
The solution to simplify-log_{10}(9*10^{-12}) is -2log_{10}(3)+12