The positive real root for the function: f(x) = ㏑(x)² - 0.7 is approximately 1.4190.
How to graph real roots of natural logarithm functions.
Logarithm functions can be defined as a way of solving inverse operation of an unknown exponential expression. A natural logarithm function (in base e) takes the form of In (x). To plot the graph of the function, let us rewrite the function in a more simplified way as:
f(x) = 2 ㏑(x) - 0.7
Using GeoGebra calculator to plot the graph; the graph have a vertical asymptote at x = 0. Since the natural log ㏑(x) is only defined for positive value on x-axis. Then, the positive real root correspond to x value on the graph where f(x) = 0.
Thus, we can conclude that the positive real root for the function: f(x) = ㏑(x)² - 0.7 is approximately 1.4190.