SOLUTION: Solve for x: 3^x+2 plus 3^x = 270 Please use steps God bless

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Question 133348: Solve for x: 3^x+2 plus 3^x = 270
Please use steps
God bless






Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28x%2B2%29%2B3%5Ex+=+270+ Start with the given equation


3%5E%28x%29%2A3%5E%282%29%2B3%5Ex+=+270+ Break up 3%5E%28x%2B2%29 using the identity x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


3%5E%28x%29%283%5E%282%29%2B1%29+=+270+ Factor out the GCF


3%5E%28x%29%289%2B1%29+=+270+ Evaluate 3%5E2 to get 9


3%5E%28x%29%2810%29+=+270+ Add


3%5E%28x%29+=+27+ Divide both sides by 10


3%5E%28x%29+=+3%5E3 Rewrite 27 as 3%5E3


Since the bases are equal, this means that the exponents are equal.

So x=3