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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= lo g_{b} (2) + 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)

= lo g_{b} (2) + 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)

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

ln ((- x + 3)^{5} (- 5 x + 7)^{4})

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

ln (\frac{x ^{2} - 3 x + 2}{x + 1})

6 lo g_{3} (u) + 3 lo g_{3} (v)

- 2 lo g_{e} (\frac{1}{4})

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