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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{5} (\frac{125}{y})

\frac{2}{3} lo g_{10} (\frac{E}{1 0 ^{4.4}})

lo g_{b} (z^{5} y)

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

lo g_{10} (\frac{z}{3} (t - 2))

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