Question

evaluate the expression without using a calculator.\\(\log_{2}(\log_{7}7)\\)\\(\log_{2}(\log_{7}7)=\square\\)

Explanation:

Step1: Evaluate inner logarithm

Recall that for any base \( a \), \( \log_a a = 1 \). So, \( \log_7 7 = 1 \).

Step2: Evaluate outer logarithm

Now we have \( \log_2 (\log_7 7)=\log_2 1 \). Recall that \( \log_a 1 = 0 \) for any \( a>0, a
eq1 \). So, \( \log_2 1 = 0 \).

Answer:

\( 0 \)