If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A. \(\frac{1}{2}\)X B. X-\(\frac{1}{4}\) C. X-\(\frac{1}{3}\) D. X-\(\frac{1}{2}\)
Correct Answer: C
Explanation
\(log_810\) = X = \(log_8{2 x 5}\) \(log_82\) + \(log_85\) = X Base 8 can be written as \(2^3\) \(log_82 = y\) therefore \(2 = 8^y\) \(y = \frac{1}{3}\) \(\frac{1}{3} = log_82\) taking \(\frac{1}{3}\) to the other side of the original equation \(log_85 = X-\frac{1}{3}\) explanation courtesy of Oluteyu and Ifechuks
