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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (x^{3} \cdot y^{12})

\frac{3}{2} + ln (\frac{3}{2})

4 ln (x) - 3 ln (y) + 5 ln (z)

2 ln (5 x)

6 lo g_{10} (m) - 2 lo g_{10} (n)

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