expand the following logarithmic expression into a sum or difference of logs. \\(\\log_{22}\\left(x^{11}y\\ri…

Explanation:

Step1: Apply Product Rule of Logs

The product rule of logarithms states that $\log_b(MN) = \log_b(M) + \log_b(N)$. For $\log_{22}(x^{11}y)$, we can split it as $\log_{22}(x^{11}) + \log_{22}(y)$.

Step2: Apply Power Rule of Logs

The power rule of logarithms states that $\log_b(M^n) = n\log_b(M)$. Applying this to $\log_{22}(x^{11})$, we get $11\log_{22}(x)$.

Step3: Combine Results

Combining the results from Step 1 and Step 2, we have $11\log_{22}(x) + \log_{22}(y)$.

Answer:

D. $11 \log_{22}(x) + \log_{22}(y)$