What is expand log_{4}((u/(v^6))^2) ?

The solution to expand log_{4}((u/(v^6))^2) is 2(log_{4}(u)-6log_{4}(v))

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expand log_{4}((u/(v^6))^2)

expand

lo g_{4} ((\frac{u}{v ^{6}})^{2})

2 (lo g_{4} (u) - 6 lo g_{4} (v))

Solution steps

lo g_{4} ((\frac{u}{v ^{6}})^{2})

Apply log rule:

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

lo g_{4} ((\frac{u}{v ^{6}})^{2}) = 2 lo g_{4} (\frac{u}{v ^{6}})

= 2 lo g_{4} (\frac{u}{v ^{6}})

Apply log rule:

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

lo g_{4} (\frac{u}{v ^{6}}) = lo g_{4} (u) - lo g_{4} (v^{6})

= 2 (lo g_{4} (u) - lo g_{4} (v^{6}))

Apply log rule:

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

lo g_{4} (v^{6}) = 6 lo g_{4} (v)

= 2 (lo g_{4} (u) - 6 lo g_{4} (v))

lo g_{4} (2 x + 3) + lo g_{4} (2 x + 15)

ln (\frac{k ^{8}}{m ^{6}})

ln (- c x)

lo g_{7} (2) + 2 lo g_{7} (3)

What is expand log_{4}((u/(v^6))^2) ?
The solution to expand log_{4}((u/(v^6))^2) is 2(log_{4}(u)-6log_{4}(v))