If log 10 to base 8 X evaluate log 5 to base 8 ... - JAMB Mathematics 1999 Question
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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Correct Option: C
(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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