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

The solution to log_{6}((x^6z)/(y^6)) is 6log_{6}(x)+log_{6}(z)-6log_{6}(y)

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simplify log_{6}((x^6z)/(y^6))

simplify

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

6 lo g_{6} (x) + lo g_{6} (z) - 6 lo g_{6} (y)

Solution steps

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

Apply log rule:

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

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

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

lo g_{6} (x^{6} z) = 6 lo g_{6} (x) + lo g_{6} (z)

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

= 6 lo g_{6} (x) + lo g_{6} (z) - 6 lo g_{6} (y)

lo g_{10} (1000 x^{3} y^{5})

lo g_{3} (x^{2} y)

ln (\frac{9}{2})

\frac{1}{3} (lo g_{10} (x) - 2 lo g_{10} (y))

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

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