SOLUTION: 3^x*3^x+1*3^x-2=243

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Question 198963: 3^x*3^x+1*3^x-2=243
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28x%29%2A3%5E%28x%2B1%29%2A3%5E%28x-2%29=243 Start with the given equation.


3%5E%28x%2Bx%2B1%29%2A3%5E%28x-2%29=243 Multiply the first two terms using the identity x%5E%28y%29%2Ax%5E%28z%29=x%5E%28y%2Bz%29


3%5E%282x%2B1%29%2A3%5E%28x-2%29=243 Combine like terms.


3%5E%282x%2B1%2Bx-2%29=243 Multiply the remaining terms using the identity x%5E%28y%29%2Ax%5E%28z%29=x%5E%28y%2Bz%29


3%5E%283x-1%29=243 Combine like terms.


3%5E%283x-1%29=3%5E5 Rewrite 243 as 3%5E5


3x-1=5 Since the bases are equal, this means that the exponents are equal.


3x=5%2B1 Add 1 to both sides.


3x=6 Combine like terms on the right side.


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x.


x=2 Reduce.


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Answer:

So the solution is x=2