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