What is log_{6}((x^3)/(y^8)) ?

The solution to log_{6}((x^3)/(y^8)) is 3log_{6}(x)-8log_{6}(y)

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simplify log_{6}((x^3)/(y^8))

simplify

lo g_{6} (\frac{x ^{3}}{y ^{8}})

3 lo g_{6} (x) - 8 lo g_{6} (y)

Solution steps

lo g_{6} (\frac{x ^{3}}{y ^{8}})

Apply log rule:

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

lo g_{6} (\frac{x ^{3}}{y ^{8}}) = lo g_{6} (x^{3}) - lo g_{6} (y^{8})

= lo g_{6} (x^{3}) - lo g_{6} (y^{8})

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

lo g_{6} (y^{8}) = 8 lo g_{6} (y)

= 3 lo g_{6} (x) - 8 lo g_{6} (y)

ln (5) + \frac{1}{2} ln (4)

2 ln (x + 1) + \frac{1}{3} ln (x) - ln (cos (x))

2 ln (x) + 6 ln (y) - 3 ln (z)

What is log_{6}((x^3)/(y^8)) ?
The solution to log_{6}((x^3)/(y^8)) is 3log_{6}(x)-8log_{6}(y)