Evaluate log of 5/7

Problem

(log_)(5/7)

Solution

1. Identify the expression as a logarithm of a quotient. By convention, (log_)() without a specified base usually refers to the common logarithm (base 10).

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

3. Expand the expression using the rule to separate the numerator and the denominator.

4. Substitute the approximate values for (log_)(5) and (log_)(7) if a decimal approximation is required. (log_)(5)≈0.69897 and (log_)(7)≈0.84510

5. Subtract the values to find the final result.

Final Answer

(log_)(5/7)=(log_)(5)−(log_)(7)≈−0.14613

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