section_path: Analytic properties/Graph of the logarithm function
section_name: Graph of the logarithm function
paragraph_text: Graph of the logarithm function
  
  As discussed above, the function log is the inverse to the exponential function x ↦ b x {\displaystyle x\mapsto b^{x}}. Therefore, their graphs correspond to each other upon exchanging the x - and the y -coordinates (or upon reflection at the diagonal line x = y), as shown at the right: a point (t, u = b) on the graph of f yields a point (u, t = log u) on the graph of the logarithm and vice versa. As a consequence, log (x) diverges to infinity (gets bigger than any given number) if x grows to infinity, provided that b is greater than one. In that case, log (x) is an increasing function. For b < 1, log (x) tends to minus infinity instead. When x approaches zero, log x goes to minus infinity for b > 1 (plus infinity for b < 1, respectively).