What is expand log_{2}((8x^2)/y) ?

The solution to expand log_{2}((8x^2)/y) is 3+2log_{2}(x)-log_{2}(y)

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expand log_{2}((8x^2)/y)

expand

lo g_{2} (\frac{8 x ^{2}}{y})

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

Solution steps

lo g_{2} (\frac{8 x ^{2}}{y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{8 x ^{2}}{y}) = lo g_{2} (8 x^{2}) - lo g_{2} (y)

= lo g_{2} (8 x^{2}) - lo g_{2} (y)

Apply log rule:

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

lo g_{2} (8 x^{2}) = lo g_{2} (8) + lo g_{2} (x^{2})

= lo g_{2} (8) + lo g_{2} (x^{2}) - lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (8) + 2 lo g_{2} (x) - lo g_{2} (y)

lo g_{2} (8) = 3

= 3 + 2 lo g_{2} (x) - lo g_{2} (y)

lo g_{3} (t) + lo g_{3} (s)

13 ln (x) - 12 ln (x^{2} + 16)

lo g_{3} (u^{2}) - lo g_{3} (v)

lo g_{2} ((\frac{b}{c})^{4})

lo g_{t} (X \cdot Y)

What is expand log_{2}((8x^2)/y) ?
The solution to expand log_{2}((8x^2)/y) is 3+2log_{2}(x)-log_{2}(y)