Sequence And Series Question 574
Question: The coefficients of $ x^{3} $ in the expansion of $ 3^{x} $ is
[Kerala (Engg.) 2005]
Options:
A) $ \frac{3^{3}}{6} $
B) $ \frac{{{(\log 3)}^{3}}}{3} $
C) $ \frac{\log (3^{3})}{6} $
D) $ \frac{{{(\log 3)}^{3}}}{6} $
E) $ \frac{3}{3,!} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ 3^{x}={e^{\log 3^{x}}} $ = $ {e^{x\log 3}} $ = $ 1+\frac{x\log 3}{1!}+\frac{x^{2}{{(\log 3)}^{2}}}{2!}+\frac{x^{3}{{(\log 3)}^{3}}}{3!}+…. $ Coefficient of $ x^{3} $ = $ \frac{{{(\log 3)}^{3}}}{3!} $ = $ \frac{{{(\log 3)}^{3}}}{6,} $ .
BETA
