To solve the exponential equation 12^x = 4 * 8^(2x), logarithms are utilized. Taking the logarithm of both sides allows for simplification using the properties of logarithms, such as log(a*b) = log(a) + log(b) and log(a^b) = b*log(a). The discussion emphasizes the importance of applying these logarithmic rules to break down the equation. Participants encourage clarity in the steps rather than assuming prior knowledge of logarithmic concepts. Ultimately, the solution hinges on correctly applying logarithmic properties to simplify and solve for x.