Question

The number of real solutions of the equation $\sin \left(e^x\right)=5^x+5^{-x}$ is (are)

• A. $0$
• B. $1$
• C. $2$
• D. Infinitely many

Answer 1

The correct option is A $0$

$\sin \left(e^x\right)$ has a max value of 1.

$5^x+5^{-x}$ has a max value of 2.

$A.M\ge G.M$

$\Rightarrow \frac{5^x+5^{-x}}{2}\ge \sqrt{5^x{.5}^{-x}}$

$5^x+5^{-x}\ge 2.$

$\therefore$ There is no point of intersection of both.

$\therefore$ No solution.