TMUA 2018 · Paper 2 · Question 11

Consider the equation $2^{x} = m x + c$ , where $m$ and $c$ are real constants.

Which of the following statements is/are true?

I The equation has a negative real solution only if $c > 1$ .

II The equation has two distinct real solutions if $c > 1$ .

III The equation has two distinct positive real solutions if and only if $c \leq 1$ .