log3 (2x-1) + log3 (5-x)=2

Question

log3 (2x-1) + log3 (5-x)=2

Answer 1

log3 (2x-1) + log3 (5-x)=log3 3^2

log3 ((2x-1)*(5-x))=log3 9

log(11x-2x^2-5)=log3 9

11x - 2x^2 - 5 = 9

2x^2-11x + 14 = 0

D=11^2 - 4*2*14=121 - 112=9

x1 = (11+3)/4=14/4=3,5

x2=(11-3)/4=8/4=2