jee-main 2022 Q72

jee-main · India · session2_29jul_shift2 Laws of Logarithms Determine Parameters of a Logarithmic Function
Let the function $f(x) = \begin{cases} \frac{\log_e(1 + 5x) - \log_e(1 + \alpha x)}{x} & \text{if } x \neq 0 \\ 10 & \text{if } x = 0 \end{cases}$ be continuous at $x = 0$. Then $\alpha$ is equal to
(1) 10
(2) $-10$
(3) 5
(4) $-5$
Let the function $f(x) = \begin{cases} \frac{\log_e(1 + 5x) - \log_e(1 + \alpha x)}{x} & \text{if } x \neq 0 \\ 10 & \text{if } x = 0 \end{cases}$ be continuous at $x = 0$. Then $\alpha$ is equal to\\
(1) 10\\
(2) $-10$\\
(3) 5\\
(4) $-5$