What is expand log_{6}((36sqrt(y))/(x^7z^2)) ?

The solution to expand log_{6}((36sqrt(y))/(x^7z^2)) is 2+log_{6}(sqrt(y))-7log_{6}(x)-2log_{6}(z)

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expand log_{6}((36sqrt(y))/(x^7z^2))

expand

lo g_{6} (\frac{36 y}{x ^{7} z ^{2}})

2 + lo g_{6} (y) - 7 lo g_{6} (x) - 2 lo g_{6} (z)

Solution steps

lo g_{6} (\frac{36 y}{x ^{7} z ^{2}})

Apply log rule:

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

lo g_{6} (\frac{36 y}{x ^{7} z ^{2}}) = lo g_{6} (36 y) - lo g_{6} (x^{7} z^{2})

= lo g_{6} (36 y) - lo g_{6} (x^{7} z^{2})

Apply log rule:

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

lo g_{6} (36 y) = lo g_{6} (36) + lo g_{6} (y), lo g_{6} (x^{7} z^{2}) = lo g_{6} (x^{7}) + lo g_{6} (z^{2})

= lo g_{6} (36) + lo g_{6} (y) - (lo g_{6} (x^{7}) + lo g_{6} (z^{2}))

Apply log rule:

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

lo g_{6} (x^{7}) = 7 lo g_{6} (x)

= lo g_{6} (36) + lo g_{6} (y) - (7 lo g_{6} (x) + lo g_{6} (z^{2}))

Apply log rule:

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

lo g_{6} (z^{2}) = 2 lo g_{6} (z)

= lo g_{6} (36) + lo g_{6} (y) - (7 lo g_{6} (x) + 2 lo g_{6} (z))

lo g_{6} (36) = 2

= 2 + lo g_{6} (y) - (7 lo g_{6} (x) + 2 lo g_{6} (z))

- (7 lo g_{6} (x) + 2 lo g_{6} (z)) : - 7 lo g_{6} (x) - 2 lo g_{6} (z)

= 2 + lo g_{6} (y) - 7 lo g_{6} (x) - 2 lo g_{6} (z)

ln (x^{y}) + ln (y^{x})

lo g_{4} (\frac{x z}{16 y ^{2}})

ln (\frac{4}{6}) - ln (\frac{1}{3})

f (x) = ln (\frac{3}{3 - x})

2 ln (x) - 2 ln (y)

What is expand log_{6}((36sqrt(y))/(x^7z^2)) ?
The solution to expand log_{6}((36sqrt(y))/(x^7z^2)) is 2+log_{6}(sqrt(y))-7log_{6}(x)-2log_{6}(z)