The value of the series x logea+ x3/3! (logea)3+x5/5! (logea)5+...... is :
cosh (x logea)
coth (x logea)
sinh (x logea)
tanh (x logea)
The sum of the series log42-log82+log162-… is
e2
loge 2+1
loge 3-2
1-loge2
Coeff. of x3 in log(1 + x + x2)
1/3
4/3
5/3
2/3
If n=3m then the coefficient of xn in the expansion of log(1+x+x2) is
n
1/n
2/n
-2/n
The coefficient of xn in the expansion of loge(1+3x+2x2) is
(-1)n-1(1+2n)/n
(-1)n(1+2n-1)/n
(-1)n-12n/n
(-1)n(2n-1)/n
If log27 (log3 x) = 1/3, then the value of x is :
3
6
9
27
The 7th term of loge(5/4) is
1/7?47
-1/7?47
1/7
-1/7
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
2x
2x2
1+2x
1-x2
If |x|
(x/1-x)+log(1-x)
(x/1-x)+log(1+x)
(x/1+x)+log(1+x)
(x/1+x)+log(1-x)