Evaluate log base 2 of log base 7 of 49

Problem

(log_2)((log_7)(49))

Solution

1. Evaluate the inner logarithmic expression (log_7)(49) by identifying the power to which the base 7 must be raised to equal 49

2. Substitute the value 7=49 into the expression, which simplifies (log_7)(49) to 2

3. Evaluate the remaining outer logarithmic expression (log_2)(2) by identifying the power to which the base 2 must be raised to equal 2

4. Simplify the expression using the property (log_b)(b)=1

Final Answer

(log_2)((log_7)(49))=1

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