What is simplify-log_{10}(3.97X10^{-11}) ?

The solution to simplify-log_{10}(3.97X10^{-11}) is -log_{10}(3.97)-log_{10}(X)+11

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simplify-log_{10}(3.97X10^{-11})

simplify

- lo g_{10} (3.97 X 1 0^{- 11})

- lo g_{10} (3.97) - lo g_{10} (X) + 11

Solution steps

- lo g_{10} (3.97 X \cdot 1 0^{- 11})

Apply log rule:

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

lo g_{10} (3.97 X \cdot 1 0^{- 11}) = lo g_{10} (3.97) + lo g_{10} (X) + lo g_{10} (1 0^{- 11})

= - (lo g_{10} (X) + lo g_{10} (3.97) + lo g_{10} (1 0^{- 11}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 11}) = - 11 lo g_{10} (10)

= - (lo g_{10} (3.97) + lo g_{10} (X) - 11 lo g_{10} (10))

11 lo g_{10} (10) = 11

= - (lo g_{10} (X) + lo g_{10} (3.97) - 11)

Distribute parentheses

= - (lo g_{10} (3.97)) - (lo g_{10} (X)) - (- 11)

Apply minus-plus rules

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

= - lo g_{10} (3.97) - lo g_{10} (X) + 11

(ln (a + x) - ln (a)) (ln (a + x) + ln (a))

lo g_{e} (\frac{n !}{( n - x ) ! x !} (Y)^{x} (1 - Y)^{n - x})

(\frac{1}{x})^{2} + lo g_{e} (2 x)

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

ln (3 x + 16) + ln (x + 4)

What is simplify-log_{10}(3.97X10^{-11}) ?
The solution to simplify-log_{10}(3.97X10^{-11}) is -log_{10}(3.97)-log_{10}(X)+11