00:03
To solve this exponential equation, we're going to need to take a logarithm of both sides, and we have a lot of different choices here.
00:10
We can use log base 10 or natural log or log base 13 or any base we want, basically.
00:17
And i'm just going to use log base 10 for this problem.
00:21
So this will be log base 10 of the left side equals log base 10 of the right side.
00:28
After doing that, we can use the power rule and bring this exponent out and multiply by it.
00:33
And make sure to put it in parentheses.
00:36
So now we have x minus 1, the quantity x minus 1, times the log of 13 equals the log of 2.
00:45
What we can do from this point, we have a couple of options, actually, in terms of order of operations.
00:53
One option would be to divide both sides of the equation by the log of 13 at this point...