What is log_{2}((ab)/(cd)) ?

The solution to log_{2}((ab)/(cd)) is log_{2}(a)+log_{2}(b)-log_{2}(c)-log_{2}(d)

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simplify log_{2}((ab)/(cd))

simplify

lo g_{2} (\frac{ab}{c d})

lo g_{2} (a) + lo g_{2} (b) - lo g_{2} (c) - lo g_{2} (d)

Solution steps

lo g_{2} (\frac{ab}{c d})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{ab}{c d}) = lo g_{2} (ab) - lo g_{2} (c d)

= lo g_{2} (ab) - lo g_{2} (c d)

lo g_{2} (ab) = lo g_{2} (a) + lo g_{2} (b)

lo g_{2} (c d) = lo g_{2} (c) + lo g_{2} (d)

= lo g_{2} (a) + lo g_{2} (b) - (lo g_{2} (c) + lo g_{2} (d))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (c) + lo g_{2} (d)) = - lo g_{2} (c) - lo g_{2} (d)

= lo g_{2} (a) + lo g_{2} (b) - lo g_{2} (c) - lo g_{2} (d)

lo g_{10} (x) - 2 lo g_{10} (y)

20 ln (\frac{1400}{1400 + 100 ( 20 )}) + 9.8 (20)

- lo g_{10} (1.6 \times 1 0^{- 4})

lo g_{4} (\frac{4}{x})

lo g_{10} (2) + lo g_{10} (12)

What is log_{2}((ab)/(cd)) ?
The solution to log_{2}((ab)/(cd)) is log_{2}(a)+log_{2}(b)-log_{2}(c)-log_{2}(d)