1. **State the problem:** Write the logarithm \( \log \left( \frac{m^4 + n}{100} \right) \) as a difference of logarithms using the quotient property. 2. **Recall the quotient property of logarithms:** \[ \log \left( \frac{a}{b} \right) = \log a - \log b \] This means the logarithm of a quotient is the difference of the logarithms of numerator and denominator. 3. **Apply the property:** \[ \log \left( \frac{m^4 + n}{100} \right) = \log (m^4 + n) - \log 100 \] 4. **Simplify \( \log 100 \):** Since \(100 = 10^2\), \[ \log 100 = \log 10^2 = 2 \log 10 = 2 \] assuming the logarithm base is 10. 5. **Final simplified expression:** \[ \log \left( \frac{m^4 + n}{100} \right) = \log (m^4 + n) - 2 \] This is the logarithm expressed as a difference and simplified as much as possible.