Evaluate log of 1/7

Problem

(log_)(1/7)

Solution

1. Identify the base of the logarithm. Since no base is specified, it is assumed to be the common logarithm, which is base 10.

2. Apply the quotient rule for logarithms, which states that (log_b)(x/y)=(log_b)(x)−(log_b)(y)

3. Substitute the values into the rule.

(log_)(1/7)=(log_)(1)−(log_)(7)

4. Simplify the expression using the property that the logarithm of 1 in any base is 0.

(log_)(1)=0

5. Combine the results to find the final logarithmic expression.

0−(log_)(7)=−(log_)(7)

Final Answer

(log_)(1/7)=−(log_)(7)

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