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jmc

algebra intermediate

Problem

If

lo g (x y^{3}) = 1

and

lo g (x^{2} y) = 1

, what is

lo g (x y)

?

Solution

We have

1 = lo g (x y^{3}) = lo g x + 3 lo g y and 1 = lo g (x^{2} y) = 2 lo g x + lo g y .

Solving yields

lo g x = \frac{2}{5}

and

lo g y = \frac{1}{5}

. Thus

lo g (x y) = lo g x + lo g y = \frac{3}{5} .

Final answer

\frac{3}{5}