What is expand log_{b}(x^2y^3) ?

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

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expand log_{b}(x^2y^3)

expand

lo g_{b} (x^{2} y^{3})

2 lo g_{b} (x) + 3 lo g_{b} (y)

Solution steps

lo g_{b} (x^{2} y^{3})

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{b} (x^{2}) = 2 lo g_{b} (x)

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

Apply log rule:

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

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

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

ln (\frac{z ^{7}}{x y})

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

lo g_{3} (z^{5} x)

lo g_{3} (\frac{4 ( x - 5 ) ^{2}}{x ^{4} ( x - 1 ) ^{3}})

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