Evaluate log base 49 of 1/7

Problem

(log_49)(1/7)

Solution

1. Identify the base and the argument of the logarithm. The base is 49 and the argument is 1/7

2. Rewrite the argument using a power of 7 Since 1/7 is the reciprocal of 7 it can be written as 7^(−1)

3. Rewrite the base using a power of 7 Since 49 is 7 squared, it can be written as 7^2

4. Apply the change of base formula or the property (log_b^n)(a^m)=m/n*(log_b)(a) Here, b=7 n=2 and m=−1

5. Substitute the values into the property.

(log_7^2)(7^(−1))=(−1)/2*(log_7)(7)

6. Simplify the expression using the identity (log_b)(b)=1

(−1)/2⋅1=−1/2

Final Answer

(log_49)(1/7)=−1/2

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