Evaluate 6^( log base 6 of 13)

Problem

6

Solution

1. Identify the structure of the expression as an exponential with a base b raised to a logarithm with the same base b

2. Apply the inverse property of logarithms, which states that for any base b>0 and b≠1 the expression b(log_b)(x) simplifies directly to x

3. Substitute the values b=6 and x=13 into the property b(log_b)(x)=x

Final Answer

6=13

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