If (log_{3}a – 2 = 3log_{3}b), express a in terms of b.
-
A.
(a = b^{3} – 3) -
B.
(a = b^{3} – 9) -
C.
(a = 9b^{3}) -
D.
(a = frac{b^{3}}{9})
Correct Answer: Option C
Explanation
(log_{3}a – 2 = 3log_{3}b)
Using the laws of logarithm, we know that ( 2 = 2log_{3}3 = log_{3}3^{2})
(therefore log_{3}a – log_{3}3^{2} = log_{3}b^{3})
= (log_{3}(frac{a}{3^{2}}) = log_{3}b^{3} implies frac{a}{9} = b^{3})
(implies a = 9b^{3})