In this study, to test the equality of means of several log-normal distributions, our aim is to investigate the effectiveness of likelihood-based methods, such as the likelihood ratio test, the Score test, and the Wald test. For this reason, we propose a Wald test based on the likelihood method. Additionally, the chi-square approximation of the Wald test statistic is often inadequate in small sample scenarios for various problems. To address this, we employ a computational approach test (CAT), known as a type of parametric bootstrap method. To assess the performance of these proposed tests, we evaluate them via their sizes and power under different numbers of groups, sample sizes, and scale parameters. Our simulation study reveals that the CAT of Wald test performs better than the others when the sample sizes and scale parameters within each group are directly proportional. We also provide a data example to illustrate the above methods.