What is simplify-log_{10}(5.2*10^{-12}) ?

The solution to simplify-log_{10}(5.2*10^{-12}) is -log_{10}(5.2)+12

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simplify-log_{10}(5.2*10^{-12})

simplify

- lo g_{10} (5.2 \cdot 1 0^{- 12})

- lo g_{10} (5.2) + 12

Decimal Notation

11.28399 \dots

Solution steps

- lo g_{10} (5.2 \cdot 1 0^{- 12})

Apply log rule:

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

lo g_{10} (5.2 \cdot 1 0^{- 12}) = lo g_{10} (5.2) + lo g_{10} (1 0^{- 12})

= - (lo g_{10} (5.2) + 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} (5.2) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (5.2) - 12)

Distribute parentheses

= - (lo g_{10} (5.2)) - (- 12)

Apply minus-plus rules

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

= - lo g_{10} (5.2) + 12

ln (8) - ln (2) - ln (\frac{1}{4})

21 ln (11) + ln (x) + ln (29)

ln (\frac{8 x - 2}{x + 2} sin (e^{2 x}))

3 ln ∣ x + 2 ∣ + 2 ln ∣ x - 2 ∣

8.314 \cdot 298 \cdot (ln (0.03 3^{5}) - ln (0.74 9^{5}))

What is simplify-log_{10}(5.2*10^{-12}) ?
The solution to simplify-log_{10}(5.2*10^{-12}) is -log_{10}(5.2)+12