Algebra
Systems of Equations
MMTS_Full_Test_15
Grade 12
Question:
The number of real solutions of $\sin\left(e^x\right)=5^x+5^{-x}$ is
Step-by-Step Solution
Key Concept: RHS: $5^x+5^{-x}\ge 2$ by AM-GM; LHS: $|\sin(e^x)|\le 1$
$5^x+5^{-x}\ge 2>1\ge\sin(e^x)$. No solutions. Answer: 1.
Correct Answer: 1