WEBVTT
1
00:00:04.240 --> 00:00:06.339 A:middle L:90%
Okay, so we have this expression that we want
2
00:00:06.339 --> 00:00:08.810 A:middle L:90%
to evaluate for F of X equals five to the
3
00:00:08.810 --> 00:00:11.949 A:middle L:90%
X power. So let's go ahead and substitute five
4
00:00:11.949 --> 00:00:14.460 A:middle L:90%
to the X in for f of X and five
5
00:00:14.460 --> 00:00:16.940 A:middle L:90%
to the X plus H in four f of X
6
00:00:16.940 --> 00:00:20.210 A:middle L:90%
plus h sweet five to the X plus H minus
7
00:00:20.210 --> 00:00:22.800 A:middle L:90%
five to the X over H. Now we want
8
00:00:22.800 --> 00:00:26.179 A:middle L:90%
to simplify that. So remember that when you see
9
00:00:26.190 --> 00:00:29.239 A:middle L:90%
five to the X plus H power, it's equivalent
10
00:00:29.239 --> 00:00:32.189 A:middle L:90%
to five to the X power power times five to
11
00:00:32.189 --> 00:00:35.750 A:middle L:90%
the age power. Think about your exponents rules.
12
00:00:36.140 --> 00:00:38.289 A:middle L:90%
And if you were given five to the X times
13
00:00:38.289 --> 00:00:40.700 A:middle L:90%
five to the age, you would add the exponents
14
00:00:41.340 --> 00:00:43.350 A:middle L:90%
. And now this is still all over H.
15
00:00:44.240 --> 00:00:46.020 A:middle L:90%
Okay, so notice that what we can do is
16
00:00:46.020 --> 00:00:48.689 A:middle L:90%
factor five to the X power out of both terms
17
00:00:48.689 --> 00:00:51.710 A:middle L:90%
in the numerator. And now we have five to
18
00:00:51.710 --> 00:00:55.009 A:middle L:90%
the X power multiplied by pi to the H power
19
00:00:55.009 --> 00:01:00.670 A:middle L:90%
minus one over H. And that's exactly what we're
20
00:01:00.670 --> 00:01:02.549 A:middle L:90%
asked to show