Questions: Find the domain of the logarithmic function and then graph the function. y=ln(2x-3) Find the domain of the function.

Solution Steps

The domain of the logarithmic function \( y = \ln(2x - 3) \) is determined by the argument of the logarithm being greater than zero: \[ 2x - 3 > 0 \] Solving for \( x \): \[ 2x > 3 \implies x > \frac{3}{2} \] Thus, the domain of the function is \( x > \frac{3}{2} \).

To graph the function \( y = \ln(2x - 3) \), we need to specify the range for \( x \) and \( y \). Since the domain is \( x > \frac{3}{2} \), we can choose a reasonable range for \( x \) starting from slightly greater than \( \frac{3}{2} \) to a larger value. For \( y \), we can choose a range that captures the behavior of the logarithmic function.

Final Answer