The value of x or if we think of it as values , will lie between 2 and 3 as for 2 or less than 2 one side of the equation becomes greater than the other and for 3 or greater than 3 , the other side of the equation becomes greater.
plotting the graph for log y/y between y=2 to 4 we get a curve which first increases then decreases, the value is almost same for 2.3 and 3.3, around 0.157
No solution!But I couldn't find any method do prove it..
ReplyDeletetry again !!
ReplyDeleteOne solution
ReplyDelete-1
what is the method?
ReplyDeleteI took log to the base x of both sides and solved it for x.
ReplyDeleteBut then x can't be -1. so it could be no solution.
ReplyDeletethere is a solution try again !
ReplyDeleteI tried constructing a graph for the equation. Infinite real roots?
ReplyDeleteTotally confused with the question. @ Outtimed can you please explain the answer.
The graph is a straight line parallel to an axis
ReplyDeleteThe value of x or if we think of it as values , will lie between 2 and 3 as for 2 or less than 2 one side of the equation becomes greater than the other and for 3 or greater than 3 , the other side of the equation becomes greater.
ReplyDeletex comes to be the xth root of (1+1/x). Thus this forms an infinite series.
ReplyDeletelog(x+1)/(x+1)=logx/x
ReplyDeletetake f(y)=logy/y
plot the graph
now check if you can find a solution or not
hint: the graph does not rise or dip monotonously!
basically we get
ReplyDelete(1+1/n)^n =n
so basically we get one root between 2 and 3 and later on as limit of left hand side is e when n approaches infinity.. so just one root..
plotting the graph for log y/y between y=2 to 4 we get a curve which first increases then decreases, the value is almost same for 2.3 and 3.3, around 0.157
ReplyDelete