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

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

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simplify log_{2}(x)y-log_{2}(x^2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Simplify

\frac{x ^{y}}{x ^{2}} : x^{y - 2}

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

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

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p^{3} - 343

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