If 0<y<213 and xy3-1=1 then 2x+23x3+25x5+.........is equal to
logy32-y3
logy31-y3
log2y31-y3
log2y31-2y3
Explanation for correct option
Step-1: Simplify the given data.
Given, xy3-1=1
⇒ x=1y3-1
Step-2 Apply componendo and Dividendo ab=cd⇔a+ba-b=c+dc-d.
⇒ x+1x-1=1+y3-11-y3+1
⇒ x+1x-1=y32-y3......i
Step-3: Apply formula: log(1+x1-x)=2[x+x33+x55+.......]
Given, 2x+23x3+25x5+.........
=21x+13x3+15x5+.........
=log1+1x1-1x
=logx+1x-1
=logy32-y3(from equation i )
Hence, correct answer is option A.
If f=x1+x2+13(x1+x2)3+15(x1+x2)5+... to ∞ and g=x−23x3+15x5+17x7−29x9+..., then f=d×g. Find 4d.