lim limits x→ 1 (log ex)1/log x is equal

Question

lim limits x→ 1 (log ex)1/log x is equal (A)  e-1  (B)  e  (C)  e2  (D)  0

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 1( log e x)1 / log x= displaystyle lim x arrow 1[ log e+ log x]1 / log x = displaystyle lim x arrow 1[1+ log x]1 / log x =e displaystyle lim x arrow 1 ( log x/ log x)=e

Q. $x \to 1 lim (l o g e x)^{1/ l o g x}$ is equal

$e^{- 1}$

$e$

$e^{2}$

$0$

$x \to 1 lim (lo g e x)^{1/ l o g x} = x \to 1 lim [lo g e + lo g x]^{1/ l o g x}$
$= x \to 1 lim [1 + lo g x]^{1/ l o g x}$
$= e^{x \to 1 lim \frac{lo g x}{lo g x}} = e$

Q. x→1lim​(logex)1/logx is equal

e−1

e

e2

0

x→1lim​(logex)1/logx=x→1lim​[loge+logx]1/logx =x→1lim​[1+logx]1/logx =ex→1lim​logxlogx​=e

Q. $x \to 1 lim (l o g e x)^{1/ l o g x}$ is equal

$e^{- 1}$

$e$

$e^{2}$

$0$

$x \to 1 lim (lo g e x)^{1/ l o g x} = x \to 1 lim [lo g e + lo g x]^{1/ l o g x}$
$= x \to 1 lim [1 + lo g x]^{1/ l o g x}$
$= e^{x \to 1 lim \frac{lo g x}{lo g x}} = e$