Tip:A–D to answerE for explanationV for videoS to reveal answer
The product of all solutions of the equation e5(log8x)2+3=x8, x > 0, is:
- A.
e8/5
(Correct Answer) - B.
e0.5
- C.
e2
- D.
e
Explanation
e5(lnx)2+3=x8
Taking ln both sides
5(lnx)2+3=8lnx
5(lnx)2−8lnx−3=0
5(lnx)2−5lnx−3lnx+3=0
(5lnx−3)(lnx−1)=0
lnx=531
x=e3/5×e1
Product =e3/5×e1=e8/5
Explanation
e5(lnx)2+3=x8
Taking ln both sides
5(lnx)2+3=8lnx
5(lnx)2−8lnx−3=0
5(lnx)2−5lnx−3lnx+3=0
(5lnx−3)(lnx−1)=0
lnx=531
x=e3/5×e1
Product =e3/5×e1=e8/5
