What is expand log_{6}((36sqrt(y))/(x^7z^3)) ?

The solution to expand log_{6}((36sqrt(y))/(x^7z^3)) is 2+log_{6}(sqrt(y))-7log_{6}(x)-3log_{6}(z)

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expand log_{6}((36sqrt(y))/(x^7z^3))

expand

lo g_{6} (\frac{36 y}{x ^{7} z ^{3}})

2 + lo g_{6} (y) - 7 lo g_{6} (x) - 3 lo g_{6} (z)

Solution steps

lo g_{6} (\frac{36 y}{x ^{7} z ^{3}})

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 ^{3}}) = lo g_{6} (36 y) - lo g_{6} (x^{7} z^{3})

= lo g_{6} (36 y) - lo g_{6} (x^{7} z^{3})

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^{3}) = lo g_{6} (x^{7}) + lo g_{6} (z^{3})

= lo g_{6} (36) + lo g_{6} (y) - (lo g_{6} (x^{7}) + lo g_{6} (z^{3}))

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^{3}))

Apply log rule:

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

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

= lo g_{6} (36) + lo g_{6} (y) - (7 lo g_{6} (x) + 3 lo g_{6} (z))

lo g_{6} (36) = 2

= 2 + lo g_{6} (y) - (7 lo g_{6} (x) + 3 lo g_{6} (z))

- (7 lo g_{6} (x) + 3 lo g_{6} (z)) : - 7 lo g_{6} (x) - 3 lo g_{6} (z)

= 2 + lo g_{6} (y) - 7 lo g_{6} (x) - 3 lo g_{6} (z)

ln (\frac{5}{x ^{2} + 9})

ln (\frac{575}{500})

lo g_{1.5} (\frac{700}{200}) - 2

- lo g_{10} (6.31 \cdot 1 0^{- 5})

ln (13) + ln (x)

What is expand log_{6}((36sqrt(y))/(x^7z^3)) ?
The solution to expand log_{6}((36sqrt(y))/(x^7z^3)) is 2+log_{6}(sqrt(y))-7log_{6}(x)-3log_{6}(z)