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

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

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

expand

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

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})

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

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

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

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

ln^{2} (x) - 2 ln (x)

lo g_{3} (\frac{9 b ^{3} y ^{2} - 7}{y ( x + 7 ) ^{2}})

x (ln^{3} (x) - 3 ln^{2} (x) + 6 ln (x) - 6)

lo g_{10} (x^{2} y^{3})

\frac{7}{2} ln (\frac{7}{2})

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