00:01
We have a function f of x equals a b plus b natural log of x.
00:05
And we want to rewrite this as g of x equals a plus c log base 5 of x.
00:13
And we want to know what c is in terms of b.
00:17
So first of all, let's get where we have the same logs.
00:21
So i'm going to start with natural log of x, which is log base e of x.
00:25
And i'm going to change this to log base 5.
00:27
So this is going to be log base 5 of x over log base 5 of e by using the change of base rule.
00:36
So i can rewrite this as a b plus b log base 5 of x over log base 5 of e.
00:46
Well, since we have log base 5 of x here, let's change that.
00:51
Let's see what log base 5 of x equals.
00:53
So we're going to say that this, um, we have a function...