Final answer:
The logarithmic equation log819 = 12 can be rewritten as the exponential equation 812 = 19 by raising the base of the logarithm to the power of the right side to get the number inside the log.
Step-by-step explanation:
The logarithmic equation given is log819 = 12. To convert this to an exponential equation, we apply the definition of a logarithm. The base of the logarithm (8 in this case) is raised to the power on the right side of the equation (12) to get the number inside the log (19). Therefore, the exponential form is 812 = 19. To write the logarithmic equation log819 = 12 as an exponential equation of the form ax = b, we need to remember that logarithms and exponentials are inverse functions.
This uses the property that the logarithm function is the inverse of the exponential function. The general form of a logarithm logba = c can be rewritten as an exponential equation bc = a, which is exactly what we've done here.