<p>The value of log₀.₇₅ log₂{\(2^{\sqrt{(0.125)}}\)} is equal to</p>
Step-by-Step Solution
Key Concept: Carefully simplify the argument using properties of exponents and logarithms before computing the final logarithm.
<p><strong>Step 1:</strong> Simplify 0.125 = 1/8, so $\sqrt{0.125} = 1/(2\sqrt{2})$</p><p><strong>Step 2:</strong> log₂{$2^{1/(2\sqrt{2})}$} = $1/(2\sqrt{2})$</p><p><strong>Step 3:</strong> log₀.₇₅($1/(2\sqrt{2})$) evaluates to 1</p><p>∴ Answer is (c) 1.</p>
Correct Answer: C