What is log_{2}(1/2 x^2y) ?

The solution to log_{2}(1/2 x^2y) is -1+2log_{2}(x)+log_{2}(y)

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simplify log_{2}(1/2 x^2y)

simplify

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

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

Solution steps

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

\frac{1}{2} = 2^{- 1}

= lo g_{2} (2^{- 1} x^{2} y)

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a^{b}) = b

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

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

Simplify

lo g_{2} (x^{2} y) : 2 lo g_{2} (x) + lo g_{2} (y)

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

Apply rule:

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

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

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

ln (\frac{e ^{3} 2}{e ^{\frac{1}{3}}}) - e^{2 l n (2)}

- ln (a) - ln (b)

ln (11 x)

\frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (y) - 4 lo g_{a} (x)

lo g_{a} (3 x y) - 5 lo g_{10} (a) (y + 2)

What is log_{2}(1/2 x^2y) ?
The solution to log_{2}(1/2 x^2y) is -1+2log_{2}(x)+log_{2}(y)