Question

The number of real solution(s) of $1+|e^x-1|=e^x(e^x-2)$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is B $1$

Two cases are possible for this equation
Case 1: $1+e^x-1=e^x(e^x-2)$
$e^{2x}-3e^x=0$
From this equation $e^x=0$ which is not possible and $e^x=3$.
Case 2: $1-e^x+1=e^x(e^x-2)$
From this equation we will get imaginary value of $e^x$ which is not possible.
So, only one solution exist.
Hence, option 'B' is correct.