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