What is simplify-log_{10}(1.3913*10^{-13}) ?

The solution to simplify-log_{10}(1.3913*10^{-13}) is -log_{10}(1.3913)+13

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simplify-log_{10}(1.3913*10^{-13})

simplify

- lo g_{10} (1.3913 \cdot 1 0^{- 13})

- lo g_{10} (1.3913) + 13

Decimal Notation

12.85657 \dots

Solution steps

- lo g_{10} (1.3913 \cdot 1 0^{- 13})

Apply log rule:

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

lo g_{10} (1.3913 \cdot 1 0^{- 13}) = lo g_{10} (1.3913) + lo g_{10} (1 0^{- 13})

= - (lo g_{10} (1.3913) + 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} (1.3913) - 13 lo g_{10} (10))

13 lo g_{10} (10) = 13

= - (lo g_{10} (1.3913) - 13)

Distribute parentheses

= - (lo g_{10} (1.3913)) - (- 13)

Apply minus-plus rules

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

= - lo g_{10} (1.3913) + 13

ln (0. 1^{2} \cdot 0. 5^{2} \cdot 1^{2} \cdot 2^{2} \cdot 4^{2})

3 ln (b) - 3 ln (a)

ln (3 x^{2}) + ln (7 y)

lo g_{6} (\frac{2 x}{y})

ln (x) + 2 ln (1 + \frac{y}{x})

What is simplify-log_{10}(1.3913*10^{-13}) ?
The solution to simplify-log_{10}(1.3913*10^{-13}) is -log_{10}(1.3913)+13