It is given that n satisfies the equation 2*log(n) - log(5*n - 24) = log(4). Show that n^2 - 20*n + 96 = 0.

Given 2log_an - log_a(5n-24) = log_a(4), we can rearrange to have all the "2logs" on one side and the "logs" on the other.So, 2log_an = log_a(4) + log_a(5n-24). Using the laws of logs (alogn = log(n^a) and loga + logb = log(a*b)) we get, log_a(n²) = log_a(4(5n-24)). Since logarithms are a one-to-one function, n² = 4(5n-24), which rearranges to n² - 20n + 96 = 0