The sum of the series log93+log273-log813+log2433-... is
1-loge2
1+loge2
loge2
1+loge3
Compute the sum:
Given : log93+log273-log813+log2433-...
log93=log3log9∵logba=logalogb⇒log93=log3log32∵logab=bloga⇒log93=12
Similarly, log273=13,log813=14.........
Thus the given series converts into
12+13-14+15...........⇒12-12+13-14+15............+12⇒1-12+13-14+15.......
We know that, loge1+x=x-x22+x33-x44+.......
Thus, the series can be written as,
⇒loge2
Therefore the sum of the series log93+log273-log813+log2433-... is loge2.
Hence option (C) is the correct option.