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: 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
\(log_85 = X\frac{1}{3}\)
explanation courtesy of Oluteyu and Ifechuks
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4 years ago
I.e log5  base8
Log(5  8)
X = log3
Applying the law of indices which if 3^0 = 1, a = 1
So log3 = 1
Applying the rule of zero power law
Log3^1 = 1/3 I.e X=log1/3