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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x^{2} + ln (e x)

lo g_{10} (2 x^{5})

ln (\frac{3}{2} e^{2 x})

ln ((3 r + 4 s) (2 r + 11 s))

1 + 5 (ln (3) - ln (4))

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