Question

evaluate the expression without using a calculator.\\(\log_{2}(\log_{7}49)\\)\\(\log_{2}(\log_{7}49)=\square\\)

Explanation:

Step1: Evaluate inner logarithm

Recall that \( \log_{a}a^{b}=b \). For \( \log_{7}49 \), note that \( 49 = 7^{2} \). So, \( \log_{7}49=\log_{7}7^{2}=2 \).

Step2: Evaluate outer logarithm

Now we have \( \log_{2}(\log_{7}49)=\log_{2}(2) \). Again, using the property \( \log_{a}a^{b}=b \) (here \( a = 2 \), \( b = 1 \) since \( 2=2^{1} \)), we get \( \log_{2}2 = 1 \).

Answer:

\( 1 \)