What is simplify-log_{10}(5*10^{-13}) ?

The solution to simplify-log_{10}(5*10^{-13}) is -log_{10}(5)+13

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simplify-log_{10}(5*10^{-13})

simplify

- lo g_{10} (5 \cdot 1 0^{- 13})

- lo g_{10} (5) + 13

Decimal Notation

12.30102 \dots

Solution steps

- lo g_{10} (5 \cdot 1 0^{- 13})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{- 13}) = lo g_{10} (5) + lo g_{10} (1 0^{- 13})

= - (lo g_{10} (5) + 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) - 13 lo g_{10} (10))

13 lo g_{10} (10) = 13

= - (lo g_{10} (5) - 13)

Distribute parentheses

= - (lo g_{10} (5)) - (- 13)

Apply minus-plus rules

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

= - lo g_{10} (5) + 13

lo g_{10} (\frac{z ^{3} y}{x ^{4}})

2 lo g_{b} (t) + \frac{1}{2} lo g_{b} (r)

lo g_{7} (x) + 2 lo g_{7} (y)

ln (3) + 2 ln (2)

3 lo g_{10} (a) - 2 lo g_{10} (b)

What is simplify-log_{10}(5*10^{-13}) ?
The solution to simplify-log_{10}(5*10^{-13}) is -log_{10}(5)+13