UPSC NDA Math Model Paper 9

Given that log5(x−2)+log5(x+3)=log514
Dropping log from the both sides we get-
⇒(x−2)×(x+3)=14
⇒x2+x−6=14
⇒x2+x−20=0
On solving the quadratic equation
x2+x−20=0
⇒(x−4)×(x+5)=0
⇒x=4 and x=−5
Therefore x=4. (negative value of x will be excluded)
Therefore, option (3) is the correct answer.