00:01
This question gives us an exponential equation and asks us to solve.
00:04
The equation it gives looks like this.
00:06
7 to the 2x minus 3 equals 7 to the 6 plus 5x.
00:19
Both of our variables here and here are in exponents.
00:24
The only tool we have right now for bringing things out of exponents is to use logarithms.
00:30
So before we do that, we need to think of what base to use on our logarithm.
00:35
Since both exponents are on a base of 7, it's probably a good idea to use log base 7.
00:41
That'll just make our calculations a lot easier.
00:45
So let's go ahead and do that.
00:46
Let's take the log base 7 of both sides.
00:50
Log 7 of 7 times raised the 2 to the x minus 3 equals log base 7 of 7 to the 6 plus 5x.
01:03
Now, when we take any log, log base a of a to the x, we know from our rules of logs that that is just equal to x...
