Simplify/Condense natural log of 2.665

Problem

ln(2.665)

Solution

1. Identify the decimal value as a fraction to see if it can be simplified into a more standard logarithmic form.

2. Convert the decimal 2.665 to a fraction by placing it over 1000

2.665=2665/1000

3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5

(2665÷5)/(1000÷5)=533/200

4. Apply the quotient rule for logarithms, ln(a/b)=ln(a)−ln(b) to express the condensed form.

ln(533/200)=ln(533)−ln(200)

Final Answer

ln(2.665)=ln(533/200)

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