00:02
So here we used a graphic utility to determine over which intervals the natural log of x is less than the log base 10 of x and when it's greater than log base 10 of x.
00:15
So we can see right here at x equals 1 there's a crossover.
00:18
To the left, the natural log is smaller.
00:22
So natural log of x is less than log base 10 of x when x is less than 1.
00:32
And of course, x can never be zero.
00:34
It approaches zero.
00:36
So we're going to have from zero to one.
00:40
And at one, they're equal.
00:42
So we also have a parentheses around the one.
00:45
After that, the natural log of x is larger.
00:48
We can see after x equals one, all along here, the red, which is our natural log of x, is higher up than the log base 10...