What is log_{2}((10^{-3})/3) ?

The solution to log_{2}((10^{-3})/3) is -3log_{2}(10)-log_{2}(3)

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simplify log_{2}((10^{-3})/3)

simplify

lo g_{2} (\frac{1 0 ^{- 3}}{3})

- 3 lo g_{2} (10) - lo g_{2} (3)

Decimal Notation

- 11.55074 \dots

Solution steps

lo g_{2} (\frac{1 0 ^{- 3}}{3})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{1 0 ^{- 3}}{3}) = lo g_{2} (1 0^{- 3}) - lo g_{2} (3)

= lo g_{2} (1 0^{- 3}) - lo g_{2} (3)

Apply log rule:

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

lo g_{2} (1 0^{- 3}) = - 3 lo g_{2} (10)

= - 3 lo g_{2} (10) - lo g_{2} (3)

ln (2) + \frac{1}{3} ln (125)

2 ln (x) + 2 ln (y)

- lo g_{10} (5.5 \cdot 1 0^{- 3})

ln (\frac{2 y ^{2}}{z ^{3}})

2 lo g_{3} (0.5) + 2 lo g_{3} (5) - 2 lo g_{3} (\frac{5}{6})

What is log_{2}((10^{-3})/3) ?
The solution to log_{2}((10^{-3})/3) is -3log_{2}(10)-log_{2}(3)