What is simplify-log_{10}(0.01*10^{-9}) ?

The solution to simplify-log_{10}(0.01*10^{-9}) is -log_{10}(0.01)+9

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simplify-log_{10}(0.01*10^{-9})

simplify

- lo g_{10} (0.01 \cdot 1 0^{- 9})

- lo g_{10} (0.01) + 9

Decimal Notation

11

Solution steps

- lo g_{10} (0.01 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (0.01 \cdot 1 0^{- 9}) = lo g_{10} (0.01) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (0.01) + lo g_{10} (1 0^{- 9}))

Apply log rule:

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

lo g_{10} (1 0^{- 9}) = - 9 lo g_{10} (10)

= - (lo g_{10} (0.01) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (0.01) - 9)

Distribute parentheses

= - (lo g_{10} (0.01)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (0.01) + 9

lo g_{2} (57.6) - lo g_{2} (1.8)

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

What is simplify-log_{10}(0.01*10^{-9}) ?
The solution to simplify-log_{10}(0.01*10^{-9}) is -log_{10}(0.01)+9