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-\(\frac{1}{2}\)

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# If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.

##### Correct Answer: Option 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

\(log_85 = X-\frac{1}{3}\)

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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-\(\frac{1}{2}\)

\(log_82\) + \(log_85\) = 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

\(log_85 = X-\frac{1}{3}\)

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