00:01
In this problem, we have given that x plus lnx is less than, so this is lnx is less than x multiplied with lnx plus 1.
00:12
Now we have to solve for x.
00:14
So we can see here this would be lnx is sent to the left hand side.
00:19
So this would be x plus lnx and this would be minus x and this is lnx.
00:25
So this would be lnx minus 1 is less than 0.
00:28
And from here we can take x common so this would be we can take one common actually so this would be x minus 1 and here we can take l n x common so this would be l and x is say here this would 1 minus x is less than 0 and here we can say this would be 1 minus x and here this would be 1 minus x t can common and this would be l n x minus 1 is less than 0 and here we have given the sign which is less than or equals so this would be less than or equals to.
01:03
So when we equated with 0, so we do have the value x is equals to this would be 1 and also this is l and x is equals to 1 that means this would be here x is equals to so this is equals to e.
01:19
So we can say this would be the value say x is equals to 1 and x is equals to e and when we plot this term say when we are putting the value which is greater than e so here this would be 1 minus so this would be value would be so this would be positive and here this would be 1 minus so this would be negative that means this would be below the graph and now when we put the value which is in between 1 and e so this would be negative and this would be negative so this would be positive here and then here this would be when we are putting the value which is less than 1...