<p>If \(y^x = 2^{x-y} \cdot 2^{y^{-x}}\) then find \(x\). (Refer MFA011 for exact expression)</p>
Step-by-Step Solution
Key Concept: Take logarithms on both sides and solve the resulting equation.
Notice that the best first move is to reveal the hidden structure in the expression. A clever move here is to rewrite the problem in the form where the standard theorem or identity applies cleanly. Taking log base 2 on both sides and simplifying the exponent equation leads to $x = 3$ as the solution. Now, we invoke the power of that idea, simplify patiently, and then check that the final answer really fits the original problem.
Correct Answer: B