What is expand log_{6}(36xy^2) ?

The solution to expand log_{6}(36xy^2) is 2+log_{6}(x)+2log_{6}(y)

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expand log_{6}(36xy^2)

expand

lo g_{6} (36 x y^{2})

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

Solution steps

lo g_{6} (36 x y^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{6} (36) = 2

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

2 ln (x) + 3 ln (y)

lo g_{10} (4 x + 1) - lo g_{10} (x)

ln (1) - ln (\frac{1}{2})

lo g_{10} (2) - lo g_{10} (3)

3 lo g_{a} (2 x + 1) - 2 lo g_{a} (2 x - 1) + 2

What is expand log_{6}(36xy^2) ?
The solution to expand log_{6}(36xy^2) is 2+log_{6}(x)+2log_{6}(y)