Question

Sa se determine valoarea lui xy stiind ca : 1/2 (lg x- lg y)= lg (x- 6/y), unde x>6\y>0

Answer 1

1/2 (lg x- lg y)= lg (x- 6/y)

<=> 1/2 • lg (x/y) = lg (x/ 6/y)

<=> lg [(x/y)^(1/2)] = lg (xy/6)

<=> lg √(x/y) = lg (xy/6)

<=> √(x/y) = xy/6 | ^2

<=> x/y = (xy)^2 / 36 | • 36y
<=>
<=> 36x = x^2 • y^3 |÷x
<=>
<=> 36 = x • y^3 = x • y • y^2