Final answer:
To determine the positive real root of ln(x²) = 0.7 graphically, plot the function y = 2ln(x) - 0.7 and find the x-coordinate where the graph intersects the x-axis.
Step-by-step explanation:
To determine the positive real root of the equation ln(x²) = 0.7 graphically, we need to create a graph of the function y = ln(x²) - 0.7. The positive real root will be the x-coordinate of the point where the graph intersects the x-axis. First, let's rewrite the equation as y = 2ln(x) - 0.7.
We can plot some points to create the graph. For example, when x = 0.5, y = 2ln(0.5) - 0.7 = -0.862. When x = 1, y = 2ln(1) - 0.7 = 0.3. When x = 2, y = 2ln(2) - 0.7 = 1.944.
Plot these points on a graph and draw a smooth curve connecting them. The positive real root can be estimated as the value of x where the curve intersects the x-axis. In this case, it appears to be slightly greater than 1.5.