What is simplify-log_{10}(5.3*10^{-13}) ?

The solution to simplify-log_{10}(5.3*10^{-13}) is -log_{10}(5.3)+13

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simplify-log_{10}(5.3*10^{-13})

simplify

- lo g_{10} (5.3 \cdot 1 0^{- 13})

- lo g_{10} (5.3) + 13

Decimal Notation

12.27572 \dots

Solution steps

- lo g_{10} (5.3 \cdot 1 0^{- 13})

Apply log rule:

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

lo g_{10} (5.3 \cdot 1 0^{- 13}) = lo g_{10} (5.3) + lo g_{10} (1 0^{- 13})

= - (lo g_{10} (5.3) + lo g_{10} (1 0^{- 13}))

Apply log rule:

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

lo g_{10} (1 0^{- 13}) = - 13 lo g_{10} (10)

= - (lo g_{10} (5.3) - 13 lo g_{10} (10))

13 lo g_{10} (10) = 13

= - (lo g_{10} (5.3) - 13)

Distribute parentheses

= - (lo g_{10} (5.3)) - (- 13)

Apply minus-plus rules

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

= - lo g_{10} (5.3) + 13

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What is simplify-log_{10}(5.3*10^{-13}) ?
The solution to simplify-log_{10}(5.3*10^{-13}) is -log_{10}(5.3)+13