00:01
Okay, so we want to prove if f is greater than or equal to 1, then the log of x is less than or equal to x minus 1.
00:08
So then what we're going to do is subtract log x from both sides.
00:15
So we need 0 less than or equal to x minus 1 minus the log of x.
00:22
In other words, that the thing on the right hand side of this is always positive, or 0.
00:33
If we put in x equals 1, then the logarithm is 0 and the first part of the term is also going to be 0, and so the answer is 0.
00:45
So the equal sign does occur.
00:48
Okay, so let's take the derivative of the right hand side.
00:53
Let's call that f of x.
00:57
So f prime of x is equal to 1 minus 1 over x...