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

The solution to expand log_{2}((2x^8)/y) is 1+8log_{2}(x)-log_{2}(y)

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

expand

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

1 + 8 lo g_{2} (x) - lo g_{2} (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

= 1 + 8 lo g_{2} (x) - lo g_{2} (y)

ln (\frac{x + 1}{4 x})

lo g_{10} (x) - 3 lo g_{10} (y) + \frac{2}{3} lo g_{10} (z)

lo g_{10} (56) - lo g_{10} (5 t)

lo g_{5} (\frac{25}{x})

lo g_{b} (\frac{2}{z ^{5} y})

What is expand log_{2}((2x^8)/y) ?
The solution to expand log_{2}((2x^8)/y) is 1+8log_{2}(x)-log_{2}(y)