Question

The domain of the function $f\left(x\right)={\log }_{x}e$ is given by $[0,\infty ]-k.$
What is $k$

• A. $1$
• B. $e$
• C. $0$
• D. $10$

Answer 1

Answer: (A), (C)

$0$
$1$

$f\left(x\right)={\log }_{x}e$

$=\frac{1}{\ln x}$

$\ln x\ne 0$

$x\ne 1$ ...(i)

Now as $x\to 0$

$\ln x\to -\infty$ ...(ii)

Thirdly domain of $\ln \left(x\right)$ cannot be less than $0.$

Hence $x>0$ ...(iii)

Therefore form (i), (ii) and (iii)

$xϵ(0,\infty )-\left\{1\right\}$

$xϵ[0,\infty )-\{0,1\}$