What is log_{3}((x^5)/(y^6)) ?

The solution to log_{3}((x^5)/(y^6)) is 5log_{3}(x)-6log_{3}(y)

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simplify log_{3}((x^5)/(y^6))

simplify

lo g_{3} (\frac{x ^{5}}{y ^{6}})

5 lo g_{3} (x) - 6 lo g_{3} (y)

Solution steps

lo g_{3} (\frac{x ^{5}}{y ^{6}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{x ^{5}}{y ^{6}}) = lo g_{3} (x^{5}) - lo g_{3} (y^{6})

= lo g_{3} (x^{5}) - lo g_{3} (y^{6})

lo g_{3} (x^{5}) = 5 lo g_{3} (x)

lo g_{3} (y^{6}) = 6 lo g_{3} (y)

= 5 lo g_{3} (x) - 6 lo g_{3} (y)

- ln (\frac{3}{4})

lo g_{a} (\frac{a ^{3} x}{y ^{2}})

lo g_{13} (13 x)

ln (\frac{7 x ^{3}}{y ^{2}})

lo g_{3} (\frac{5}{q ^{2} p})

What is log_{3}((x^5)/(y^6)) ?
The solution to log_{3}((x^5)/(y^6)) is 5log_{3}(x)-6log_{3}(y)