What is 3log_{b}(x)+1/2 log_{b}(y) ?

The solution to 3log_{b}(x)+1/2 log_{b}(y) is log_{b}(x^3y^{1/2})

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simplify 3log_{b}(x)+1/2 log_{b}(y)

simplify

3 lo g_{b} (x) + \frac{1}{2} lo g_{b} (y)

lo g_{b} (x^{3} y^{\frac{1}{2}})

Solution steps

3 lo g_{b} (x) + \frac{1}{2} lo g_{b} (y)

Apply log rule:

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

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

= lo g_{b} (x^{3}) + \frac{1}{2} lo g_{b} (y)

Apply log rule:

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

\frac{1}{2} lo g_{b} (y) = lo g_{b} (y^{\frac{1}{2}})

= lo g_{b} (x^{3}) + lo g_{b} (y^{\frac{1}{2}})

Apply log rule:

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

lo g_{b} (x^{3}) + lo g_{b} (y^{\frac{1}{2}}) = lo g_{b} (x^{3} y^{\frac{1}{2}})

= lo g_{b} (x^{3} y^{\frac{1}{2}})

lo g_{8} (x) - lo g_{8} (50)

\frac{18}{5} lo g_{\frac{4}{5}} (2)

ln (y - 2) + ln (y + 2)

\frac{1}{3} ln (\frac{x ^{2} + 1}{5}) - \frac{1}{3} ln (\frac{x ^{2} + 4}{5})

ln (\frac{48}{5})

What is 3log_{b}(x)+1/2 log_{b}(y) ?
The solution to 3log_{b}(x)+1/2 log_{b}(y) is log_{b}(x^3y^{1/2})