What is log_{2}(2xy) ?

The solution to log_{2}(2xy) is 1+log_{2}(x)+log_{2}(y)

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simplify log_{2}(2xy)

simplify

lo g_{2} (2 x y)

1 + lo g_{2} (x) + lo g_{2} (y)

Solution steps

lo g_{2} (2 x y)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (2 x y) = lo g_{2} (2) + lo g_{2} (x y)

= lo g_{2} (2) + lo g_{2} (x y)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (x y)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (x y) = lo g_{2} (x) + lo g_{2} (y)

= 1 + (lo g_{2} (x) + lo g_{2} (y))

Apply rule:

a + (b + c) = a + b + c

1 + (lo g_{2} (x) + lo g_{2} (y)) = 1 + lo g_{2} (x) + lo g_{2} (y)

= 1 + lo g_{2} (x) + lo g_{2} (y)

lo g_{10} (9) + lo g_{10} (10) - lo g_{10} (5)

ln (3) - ln (27)

0.5 ln (x^{2} + 1) - 4 ln (0.5) - 0.5 (ln (x + 4) + ln (x))

ln (\frac{e ^{6}}{3})

ln (\frac{- 4.362}{- 4.732})