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.