The coefficient of ${x^3}$ in the expansion of ${3^x}$ is

$\frac{{{{\left( {\log 3} \right)}^3}}}{3}$

$\frac{{\log {{\left( 3 \right)}^3}}}{6}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

The coefficient of

{x^3}

in the expansion of

{3^x}

View answer and explanation

Correct option: D

\frac{{{{\left( {\log 3} \right)}^3}}}{6}

Option D (

\frac{{{{\left( {\log 3} \right)}^3}}}{6}

) is correct because it is the coefficient of

{x^3}

in the Maclaurin series expansion of

{3^x}

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}