What is 1/3 log_{2}(y)-log_{2}(x)-log_{2}(x+2) ?

The solution to 1/3 log_{2}(y)-log_{2}(x)-log_{2}(x+2) is log_{2}((\sqrt[3]{y})/(x(x+2)))

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simplify 1/3 log_{2}(y)-log_{2}(x)-log_{2}(x+2)

simplify

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

Solution steps

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

Apply log rule:

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

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

= lo g_{2} (y^{\frac{1}{3}}) - lo g_{2} (x) - lo g_{2} (x + 2)

Apply log rule:

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

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

= lo g_{2} (\frac{y ^{\frac{1}{3}}}{x}) - lo g_{2} (x + 2)

Apply log rule:

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

lo g_{2} (\frac{y ^{\frac{1}{3}}}{x}) - lo g_{2} (x + 2) = lo g_{2} \frac{\frac{y ^{\frac{1}{3}}}{x}}{x + 2}

= lo g_{2} \frac{\frac{y ^{\frac{1}{3}}}{x}}{x + 2}

Simplify

\frac{\frac{y ^{\frac{1}{3}}}{x}}{x + 2} : \frac{y ^{\frac{1}{3}}}{x ( x + 2 )}

= lo g_{2} (\frac{y ^{\frac{1}{3}}}{x ( x + 2 )})

Apply exponent rule:

ln (\frac{74}{130})

lo g_{3} (\frac{x ^{2} - 14 x + 24}{4}) - 5 x + 2

2 ln (x) + 7 ln (y) - 3 ln (z)

ln (3) + 2 ln (x)

lo g_{9} (4) - lo g_{9} (7)

What is 1/3 log_{2}(y)-log_{2}(x)-log_{2}(x+2) ?
The solution to 1/3 log_{2}(y)-log_{2}(x)-log_{2}(x+2) is log_{2}((\sqrt[3]{y})/(x(x+2)))