1. The problem is to understand what \( \ln \) means. 2. \( \ln \) stands for the natural logarithm, which is the logarithm to the base \( e \), where \( e \approx 2.71828 \). 3. The natural logarithm \( \ln(x) \) answers the question: "To what power must we raise \( e \) to get \( x \)?" In other words, \( \ln(x) = y \) means \( e^y = x \). 4. Important rules for \( \ln \): - \( \ln(1) = 0 \) because \( e^0 = 1 \). - \( \ln(e) = 1 \) because \( e^1 = e \). - \( \ln(ab) = \ln(a) + \ln(b) \). - \( \ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b) \). - \( \ln(a^r) = r \ln(a) \). 5. \( \ln \) is defined only for positive real numbers \( x > 0 \). Final answer: \( \ln(x) \) is the natural logarithm, the power to which \( e \) must be raised to get \( x \).