SOLUTION: {{{9^(x+2)=240+9^x}}}

Question 513557:

Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
The first thing to recognize is that by definition of properties of exponents. That is equivalent to saying on the left hand side of your equation.

You now have . If you subtract from both sides, you have . The left hand side simplifies to (you could factor out and be left with or you could recognize that 81*something-same something=80*something).

Now, you have . Divide by 80 on both sides and get . A couple of ways to think about this:
1) 9 to what power gives me 3?
2) The square root of 9 is 3; what's the exponent for square root?
3) =?
4) Get like bases. 9 is the same as , so this could be written as , or . Since the bases are equal, the exponents must be equal, and , so .

No matter how you do it, you should get .
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