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

The solution to expand log_{2}(2xy^2) is 1+log_{2}(x)+2log_{2}(y)

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expand log_{2}(2xy^2)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

= 1 + lo g_{2} (x) + 2 lo g_{2} (y)

ln (x) - 3 [4 ln (x - 6) - ln (x + 6)]

ln (7 x)

lo g_{4} (9 x y)

3 - 3 lo g_{6} (2) - lo g_{6} (9)

What is expand log_{2}(2xy^2) ?
The solution to expand log_{2}(2xy^2) is 1+log_{2}(x)+2log_{2}(y)