SOLUTION: Solve for x in the equation 3^(2x-1)+2*3^(2x+1)=171

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Question 1195399: Solve for x in the equation 3^(2x-1)+2*3^(2x+1)=171
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


3%5E%282x-1%29%2B2%2A3%5E%282x%2B1%29=171

Make both exponents the same by rewriting 3%5E%282x%2B1%29 as %283%5E2%29%283%5E%282x-1%29%29.

3%5E%282x-1%29%2B2%283%5E2%29%283%5E%282x-1%29%29=171
3%5E%282x-1%29%2B18%2A3%5E%282x-1%29=171
19%2A3%5E%282x-1%29=171
3%5E%282x-1%29=171%2F19=9=3%5E2
2x-1=2
2x=3
x=3%2F2

ANSWER: x=3/2

CHECK:
2x-1=3-1=2
2x+1=3+1=4
3^2+2*3^4=9+2(81)=9+162=171