What is simplify-log_{10}(4.2*10^{-12}) ?

The solution to simplify-log_{10}(4.2*10^{-12}) is -log_{10}(4.2)+12

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simplify-log_{10}(4.2*10^{-12})

simplify

- lo g_{10} (4.2 \cdot 1 0^{- 12})

- lo g_{10} (4.2) + 12

Decimal Notation

11.37675 \dots

Solution steps

- lo g_{10} (4.2 \cdot 1 0^{- 12})

Apply log rule:

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

lo g_{10} (4.2 \cdot 1 0^{- 12}) = lo g_{10} (4.2) + lo g_{10} (1 0^{- 12})

= - (lo g_{10} (4.2) + 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} (4.2) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (4.2) - 12)

Distribute parentheses

= - (lo g_{10} (4.2)) - (- 12)

Apply minus-plus rules

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

= - lo g_{10} (4.2) + 12

5 ln (\frac{y}{x} + 1) - 4 ln (\frac{y}{x} + 2) + ln (x)

ln (9) - 3 ln (x) - 2 ln (y)

lo g_{10} (2) + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (\frac{4.1 \cdot 1 0 ^{8}}{1.7 \cdot 1 0 ^{7}})

3 ln (\frac{11}{10.5})

What is simplify-log_{10}(4.2*10^{-12}) ?
The solution to simplify-log_{10}(4.2*10^{-12}) is -log_{10}(4.2)+12