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Write the expression ln 3-ln 5 as a single logarithm in simplest form without any negative exponents. Answer: ln(◻)

Write the expression ln⁡3−ln⁡5 \ln 3-\ln 5 as a single logarithm in simplest form without any negative exponents.\newlineAnswer: ln⁡(□) \ln (\square)

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Full solution

Q. Write the expression ln⁡3−ln⁡5 \ln 3-\ln 5 as a single logarithm in simplest form without any negative exponents.\newlineAnswer: ln⁡(□) \ln (\square)
  1. Apply logarithm rule: Apply the logarithm rule for the difference of logarithms.\newlineThe rule states that ln⁡(a)−ln⁡(b)=ln⁡(ab)\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right).\newlineSo, ln⁡3−ln⁡5\ln 3 - \ln 5 can be rewritten as ln⁡(35)\ln\left(\frac{3}{5}\right).
  2. Simplify expression: Simplify the expression if possible.\newlineThe fraction 35\frac{3}{5} is already in simplest form, so no further simplification is needed.

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