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This problem says solve the following equations analytically with exact answers.
00:04
And we're given 9 raised to the 2x equals 1 over 81, and log base 2 of 3 minus x minus log base 2 of 3 plus x equal to 1.
00:12
And for our first equation, we want to try to make our bases match, because we do have a base of 9 here.
00:17
And we have 1 over 81, where 81 can be written with a base of 9.
00:21
So we'll leave 9 raised to the 2x on the left side, and we're going to change 81 to be 9 squared.
00:28
But for us to have a common base, we can't leave that 9 in the bottom of the fraction.
00:32
So we're going to make that not only just the second power, but the negative second power, which would take our 9 to the bottom of the fraction and make it 9 squared.
00:39
In other words, 1 over 9 squared, which is what we're seeing here.
00:42
So now that we have our bases equivalent, we can focus on our exponents and set 2x equal to negative 2 and solve.
00:51
And we can solve by dividing by 2 on both sides to isolate x, which gives us the x value solution of negative 1...