Evaluate log of 9/300

Problem

(log_)(9/300)

Solution

1. Simplify the fraction inside the logarithm by dividing both the numerator and the denominator by their greatest common divisor, which is 3

9/300=3/100

2. Apply the quotient rule for logarithms, which states that (log_)(a/b)=(log_)(a)−(log_)(b)

(log_)(3/100)=(log_)(3)−(log_)(100)

3. Evaluate the term (log_)(100) by recognizing that 100=10 and assuming the common logarithm (base 10.

(log_)(100)=2

4. Substitute the value back into the expression to find the final exact form.

(log_)(3)−2

5. Calculate the approximate decimal value using (log_)(3)≈0.4771

0.4771−2=−1.5229

Final Answer

(log_)(9/300)=(log_)(3)−2≈−1.5229

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