What is expand log_{7}(((uw)/(v^4))^6) ?

The solution to expand log_{7}(((uw)/(v^4))^6) is 6(log_{7}(uw)-4log_{7}(v))

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expand log_{7}(((uw)/(v^4))^6)

expand

lo g_{7} ((\frac{u w}{v ^{4}})^{6})

6 (lo g_{7} (u w) - 4 lo g_{7} (v))

Solution steps

lo g_{7} ((\frac{u w}{v ^{4}})^{6})

Apply log rule:

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

lo g_{7} ((\frac{u w}{v ^{4}})^{6}) = 6 lo g_{7} (\frac{u w}{v ^{4}})

= 6 lo g_{7} (\frac{u w}{v ^{4}})

Apply log rule:

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

lo g_{7} (\frac{u w}{v ^{4}}) = lo g_{7} (u w) - lo g_{7} (v^{4})

= 6 (- lo g_{7} (v^{4}) + lo g_{7} (u w))

Apply log rule:

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

lo g_{7} (v^{4}) = 4 lo g_{7} (v)

= 6 (lo g_{7} (u w) - 4 lo g_{7} (v))

ln (7 x) - ln (7)

ln (\frac{e ^{x}}{x ^{7}})

lo g_{a} (\frac{x ^{8}}{y z ^{9}})

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

lo g_{6} (\frac{1}{6} m n^{2})

What is expand log_{7}(((uw)/(v^4))^6) ?
The solution to expand log_{7}(((uw)/(v^4))^6) is 6(log_{7}(uw)-4log_{7}(v))