The number of value(s) of x satisfying the equation 4 log 2( ln x)-1+ ln 3 x-3 ln 2 x-5 ln x+7=0

Question

The number of value(s) of x satisfying the equation 4 log 2( ln x)-1+ ln 3 x-3 ln 2 x-5 ln x+7=0  (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

( ln x)2-1+( ln x-1)( ln 2 x -2 ln x -7)=0 ( ln x -1)[( ln x +1)+( ln 2 x -2 ln x -7)]=0 ∴ ln x =1 ; ln x =-2 ; ln x =3 But ln x =1 ln x =3 text are acceptable only ∴ x = e x = e 3

Q. The number of value(s) of $x$ satisfying the equation $4^{l o g_{2} (l n x)} - 1 + ln^{3} x - 3 ln^{2} x - 5 ln x + 7 = 0$

0

1

2

3

$(ln x)^{2} - 1 + (ln x - 1) (ln^{2} x - 2 ln x - 7) = 0$
$(ln x - 1) [(ln x + 1) + (ln^{2} x - 2 ln x - 7)] = 0$
$∴ ln x = 1; ln x = - 2; ln x = 3$
But $ln x = 1$ & $ln x = 3 are acceptable only$
$∴ x = e$ & $x = e^{3}$

Q. The number of value(s) of x satisfying the equation 4log2​(lnx)−1+ln3x−3ln2x−5lnx+7=0

0

1

2

3

(lnx)2−1+(lnx−1)(ln2x−2lnx−7)=0 (lnx−1)[(lnx+1)+(ln2x−2lnx−7)]=0 ∴lnx=1;lnx=−2;lnx=3 But lnx=1 & lnx=3 are acceptable only ∴x=e & x=e3

Q. The number of value(s) of $x$ satisfying the equation $4^{l o g_{2} (l n x)} - 1 + ln^{3} x - 3 ln^{2} x - 5 ln x + 7 = 0$

$(ln x)^{2} - 1 + (ln x - 1) (ln^{2} x - 2 ln x - 7) = 0$
$(ln x - 1) [(ln x + 1) + (ln^{2} x - 2 ln x - 7)] = 0$
$∴ ln x = 1; ln x = - 2; ln x = 3$
But $ln x = 1$ & $ln x = 3 are acceptable only$
$∴ x = e$ & $x = e^{3}$