SOLUTION: solve 9^(2x + 1) = 27^x

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Question 46234: solve 9^(2x + 1) = 27^x
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
these types of questions look really hard but at very simple (usually :-) ).

The thing to spot is that the 2 base numbers, here 9 and 27 are both powers of 3. We will convert the numbers to 3 and then we will have "3 to the power of whatever" equals "3 to the power of something else". So, the 2 powers must be the same thing.

+9%5E%282x+%2B+1%29+=+27%5Ex+
+%283%5E2%29%5E%282x+%2B+1%29+=+%283%5E3%29%5Ex+
+3%5E%282%282x%2B1%29%29+=+3%5E%283x%29+

So now we can say that
+2%282x%2B1%29+=+3x+
+4x%2B2+=+3x+
+x%2B2+=+0+
+x+=+-2+

CHECK:
+9%5E%282%28-2%29+%2B+1%29+=+27%5E%28-2%29+
+9%5E%28-4%2B1%29+=+27%5E%28-2%29+
+9%5E%28-3%29+=+27%5E%28-2%29+
+1%2F9%5E%283%29+=+1%2F27%5E%282%29+
+1%2F%283%5E2%29%5E%283%29+=+1%2F%283%5E3%29%5E%282%29+
+1%2F%283%5E6%29+=+1%2F%283%5E6%29+

so we are correct.

jon