What is expand log_{8}(((u^3)/v)^2) ?

The solution to expand log_{8}(((u^3)/v)^2) is 2(3log_{8}(u)-log_{8}(v))

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expand log_{8}(((u^3)/v)^2)

expand

lo g_{8} ((\frac{u ^{3}}{v})^{2})

2 (3 lo g_{8} (u) - lo g_{8} (v))

Solution steps

lo g_{8} ((\frac{u ^{3}}{v})^{2})

Apply log rule:

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

lo g_{8} ((\frac{u ^{3}}{v})^{2}) = 2 lo g_{8} (\frac{u ^{3}}{v})

= 2 lo g_{8} (\frac{u ^{3}}{v})

Apply log rule:

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

lo g_{8} (\frac{u ^{3}}{v}) = lo g_{8} (u^{3}) - lo g_{8} (v)

= 2 (lo g_{8} (u^{3}) - lo g_{8} (v))

Apply log rule:

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

lo g_{8} (u^{3}) = 3 lo g_{8} (u)

= 2 (3 lo g_{8} (u) - lo g_{8} (v))

ln (\frac{x}{e ^{4 x}})

ln (\frac{e ^{8}}{15})

- \frac{1}{4} \cdot lo g_{2} (\frac{1}{4}) - \frac{3}{4} \cdot lo g_{2} (\frac{3}{4})

lo g_{b} (\frac{1}{72})

What is expand log_{8}(((u^3)/v)^2) ?
The solution to expand log_{8}(((u^3)/v)^2) is 2(3log_{8}(u)-log_{8}(v))