Evaluate ${\log }_{2}2{\log }_{2}2$.

• A. $1$
• B. $4$
• C. $2$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Identify the expression to evaluate: \(\log_{2} \left( 2^{\log_{2} 2} \right)\).
2. Recall that \(\log_{2} 2 = 1\) because 2 raised to the power 1 equals 2.
3. Substitute \(\log_{2} 2\) with 1 inside the exponent: the expression becomes \(\log_{2} \left( 2^{1} \right)\).
4. Use the logarithm power rule: \(\log_{b} (b^{x}) = x\), so \(\log_{2} \left( 2^{1} \right) = 1\).
5. Therefore, the value of the original expression is 1.