What is simplify-log_{10}(4*10^{-13}) ?

The solution to simplify-log_{10}(4*10^{-13}) is -2log_{10}(2)+13

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simplify-log_{10}(4*10^{-13})

simplify

- lo g_{10} (4 \cdot 1 0^{- 13})

- 2 lo g_{10} (2) + 13

Decimal Notation

12.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 13})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 13}) = lo g_{10} (4) + lo g_{10} (1 0^{- 13})

= - (lo g_{10} (4) + 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} (4) - 13 lo g_{10} (10))

13 lo g_{10} (10) = 13

= - (lo g_{10} (4) - 13)

lo g_{10} (4) = 2 lo g_{10} (2)

= - (2 lo g_{10} (2) - 13)

Distribute parentheses

= - (2 lo g_{10} (2)) - (- 13)

Apply minus-plus rules

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

= - 2 lo g_{10} (2) + 13

ln (\frac{2 x}{x ^{2} - 1})

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x + 8)

- ln (2 π) - \frac{1}{2} (0. 1^{2} + 0. 3^{2}) - 2.23804

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

- lo g_{10} (8.04 \cdot 1 0^{- 8})

What is simplify-log_{10}(4*10^{-13}) ?
The solution to simplify-log_{10}(4*10^{-13}) is -2log_{10}(2)+13