A) \[\frac{{{3}^{3}}}{6}\]
B) \[\frac{{{(\log 3)}^{3}}}{3}\]
C) \[\frac{\log ({{3}^{3}})}{6}\]
D) \[\frac{{{(\log 3)}^{3}}}{6}\]
E) \[\frac{3}{3\,!}\]
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 \[{{x}^{3}}\] = \[\frac{{{(\log 3)}^{3}}}{3!}\]=\[\frac{{{(\log 3)}^{3}}}{6\,}\].
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