0:00
All right.
00:01
We are going to be using properties of logarithms to solve, and we'll have to switch kind of between exponential and log form to help us do this.
00:11
So in the properties of logs, when you add and then you rewrite something as one log, you bring it together with multiplication.
00:19
So here, if i want to write this using just one log, i have my log.
00:25
And then i'm going to multiply my 2 to the x times my 2 to the 2.
00:32
And so here, bringing together my logs, i use multiplication because i had addition, and i have 2 to the x times 2 to the 2x.
00:43
That equals 5.
00:46
At that point, now i'm looking at my properties of exponents.
00:51
If i'm multiplying things with the same base, which they both have a base of 2, i get to add my exponents.
00:57
So here i have log 2x plus 2x is 3x.
01:05
And that equals 5.
01:08
If i have a log and it's wrote without a base, it actually has a base of 10.
01:14
So that is just my common lot.
01:17
And so i'm going to add my 10 and as my base.
01:19
And then i have to remember that to put something from log form into exponential, i take my base.
01:27
I raise it to the outside and it equals the inside.
01:30
So now i have 10 to the fifth, equaling 3x.
01:39
Oops, hold on.
01:41
2 to the 3x, not 3x.
01:43
That would make our problem a little bit shorter.
01:45
So 10 to the 5th equals 2 to the 3x.
01:51
10 to the 5th is something i can simplify.
01:53
And so that is 100 ,000...