What is expand log_{6}(((x+3)^2)/(3y^3)) ?

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

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expand log_{6}(((x+3)^2)/(3y^3))

expand

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}})

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

Solution steps

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}})

Apply log rule:

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

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}}) = lo g_{6} ((x + 3)^{2}) - lo g_{6} (3 y^{3})

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

Apply log rule:

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

lo g_{6} ((x + 3)^{2}) = 2 lo g_{6} (x + 3)

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

Apply log rule:

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

lo g_{6} (3 y^{3}) = lo g_{6} (3) + lo g_{6} (y^{3})

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

Apply log rule:

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

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

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

- (lo g_{6} (3) + 3 lo g_{6} (y)) : - lo g_{6} (3) - 3 lo g_{6} (y)

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

2000 [ln (5) - ln (4)]

\frac{1}{3} ln (x) - 7 ln (y) + \frac{ln ( z )}{2}

ln (x - 1) + ln (x + 2)

ln (21.3619) - ln (58.8018)

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