What is expand log_{6}((u/(v^6))^5) ?

The solution to expand log_{6}((u/(v^6))^5) is 5(log_{6}(u)-6log_{6}(v))

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expand log_{6}((u/(v^6))^5)

expand

lo g_{6} ((\frac{u}{v ^{6}})^{5})

5 (lo g_{6} (u) - 6 lo g_{6} (v))

Solution steps

lo g_{6} ((\frac{u}{v ^{6}})^{5})

Apply log rule:

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

lo g_{6} ((\frac{u}{v ^{6}})^{5}) = 5 lo g_{6} (\frac{u}{v ^{6}})

= 5 lo g_{6} (\frac{u}{v ^{6}})

Apply log rule:

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

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

= 5 (lo g_{6} (u) - lo g_{6} (v^{6}))

Apply log rule:

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

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

= 5 (lo g_{6} (u) - 6 lo g_{6} (v))

- ln (1 - x) + ln (1 - y)

ln (13) - ln (5)

ln (2) + ln (3) + ln (5)

ln (7 x^{2} - 5) - ln (x^{2})

\frac{1}{2} ln (\frac{386}{530})

What is expand log_{6}((u/(v^6))^5) ?
The solution to expand log_{6}((u/(v^6))^5) is 5(log_{6}(u)-6log_{6}(v))