What is expand log_{2}((x/y)^5) ?

The solution to expand log_{2}((x/y)^5) is 5(log_{2}(x)-log_{2}(y))

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expand log_{2}((x/y)^5)

expand

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

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

Solution steps

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

Apply log rule:

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

lo g_{2} ((\frac{x}{y})^{5}) = 5 lo g_{2} (\frac{x}{y})

= 5 lo g_{2} (\frac{x}{y})

Apply log rule:

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

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

= 5 (lo g_{2} (x) - lo g_{2} (y))

ln (\frac{0.5}{- 0.15})

ln (1 + e^{- x}) - ln (1 + e^{x})

ln (\frac{729}{441})

ln (4) - ln (8)

lo g_{10} (x^{7} z)

What is expand log_{2}((x/y)^5) ?
The solution to expand log_{2}((x/y)^5) is 5(log_{2}(x)-log_{2}(y))