- Home
- Standard 11
- Mathematics
4-2.Quadratic Equations and Inequations
normal
સમીકરણ $ln(lnx)$ = $log_xe$ ના કેટલા ઉકેલો મળે?
A
$0$
B
$1$
C
$2$
D
અનંત
Solution
$\ell n(\ell nx) = {\log _x}e \Rightarrow \ell n(\ell nx) = \frac{1}{{\ell nx}}$
Let $\ell n{\rm{x}} = {\rm{t}}$
$\ell n{\rm{t}} = \frac{1}{{\rm{t}}}$
it has one solution
$t \in(1, e)$
$\Rightarrow \ell n x<1$ (Reject)
$\because \ell n({\mathop{\rm nx}\nolimits} ) < 0$ but $\log _{x} e>0$
Standard 11
Mathematics
