1. \( y=10 \ln x \) 3. \( y=\ln x^{1 / 2} \)

It looks like you have two equations involving logarithms. Let's analyze each one. 1. **Equation 1**: \( y = 10 \ln x \) This equation represents a linear relationship between \( y \) and \( \ln x \). The coefficient of \( \ln x \) is 10, which means that for every unit increase in \( \ln x \), \( y \) increases by 10. The graph of this equation will be a straight line that passes through the origin (0,0) since \( \ln(1) = 0 \). 2. **Equation 2**: \( y = \ln x^{1/2} \) This equation can be simplified using the properties of logarithms. Specifically, we can use the power rule of logarithms, which states that \( \ln(a^b) = b \ln a \). Therefore, we can rewrite the equation as: \[ y = \ln x^{1/2} = \frac{1}{2} \ln x \] This means that \( y \) is half of \( \ln x \). The graph of this equation will also be a straight line, but it will have a slope of \( \frac{1}{2} \) compared to the slope of 10 in the first equation. ### Summary: - The first equation \( y = 10 \ln x \) has a slope of 10. - The second equation \( y = \frac{1}{2} \ln x \) has a slope of \( \frac{1}{2} \). If you have any specific questions or need further analysis, feel free to ask!