Simplify/Condense log of 7/100

Problem

(log_)(7/100)

Solution

1. Identify the expression as a logarithm of a quotient.

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

3. Substitute the values into the rule to get (log_)(7)−(log_)(100)

4. Evaluate the term (log_)(100) by recognizing that 100=10^2 so (log_10)(10^2)=2

5. Simplify the final expression by replacing (log_)(100) with 2

Final Answer

(log_)(7/100)=(log_)(7)−2

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