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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{5} (v^{5}) = 5 lo g_{5} (v)

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

ln (\frac{7}{9})

ln (\frac{1}{x ^{5}})

lo g_{4} (x y^{8} z^{4})

ln (\frac{11}{8})

lo g_{5} (\frac{4 x}{36 y ^{4}})

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