Eamcet - Maths - Logarithmic Series Question And Answers

If log27 (log3 x) = 1/3, then the value of x is :

A.  3

B.  6

C.  9

D.  27

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Coeff. of x3 in log(1 + x + x2)

A.  1/3

B.  4/3

C.  5/3

D.  2/3

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The value of the series x logea+ x3/3! (logea)3+x5/5! (logea)5+...... is :

A.  cosh (x logea)

B.  coth (x logea)

C.  sinh (x logea)

D.  tanh (x logea)

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The coefficient of xn in the expansion of loge(1+3x+2x2) is

A.  (-1)n-1(1+2n)/n

B.  (-1)n(1+2n-1)/n

C.  (-1)n-12n/n

D.  (-1)n(2n-1)/n

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The 7th term of loge(5/4) is

A.  1/7?47

B.  -1/7?47

C.  1/7

D.  -1/7

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If n=3m then the coefficient of xn in the expansion of log(1+x+x2) is

A.  n

B.  1/n

C.  2/n

D.  -2/n

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If x is very small and neglecting x3 and higher powers of x then the expansion of log(1+x2)-log(1+x)-log(1-x) as ascending powers of x is

A.  2x

B.  2x2

C.  1+2x

D.  1-x2

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If |x|

A.  (x/1-x)+log(1-x)

B.  (x/1-x)+log(1+x)

C.  (x/1+x)+log(1+x)

D.  (x/1+x)+log(1-x)

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The sum of the series log42-log82+log162-… is

A.  e2

B.  loge 2+1

C.  loge 3-2

D.  1-loge2

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