Find, without using logarithm tables, the value of (frac{log_3 27 – log_{frac{1}{4}} 64}{log_3 frac{1}{81}})
-
A.
(frac{-3}{9}) -
B.
(frac{-3}{2}) -
C.
(frac{6}{11}) -
D.
(frac{43}{78})
Correct Answer: Option B
Explanation
(frac{log_{3} 27 – log_{frac{1}{4}} 64}{log_{3} (frac{1}{81})})
(log_{3} 27 = log_{3} 3^{3} = 3log_{3} 3 = 3)
(log_{frac{1}{4}} 64 = log_{frac{1}{4}} (frac{1}{4})^{-3} = -3)
(log_{3} (frac{1}{81}) = log_{3} 3^{-4} = -4)
(therefore frac{log_{3} 27 – log_{frac{1}{4}} 64}{log_{3} (frac{1}{81})} = frac{3 – (-3)}{-4})
= (frac{6}{-4} = frac{-3}{2})