Question

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

• A. $1$
• B. $2$
• C. $5$
• D. None of the above

Answer 1

Answer: (D)

None of the above

As $5^x,5^{-x}$ are positive terms, we will apply $AM\ge GM$

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

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

But $\text{sin}{e}^x\le 1$

Number of real roots are 0