SOLUTION: Solve for x algebraically: 3^𝑥 + 3^𝑥+1 = 11^𝑥 + 11^𝑥+1 Leave your answer as an exact value (do not round).

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Question 1162221: Solve for x algebraically: 3^𝑥 + 3^𝑥+1 = 11^𝑥 + 11^𝑥+1
Leave your answer as an exact value (do not round).
Answer by ikleyn(53765) About Me  (Show Source):
You can put this solution on YOUR website!
.

3%5Ex + 3%5E%28x%2B1%29 = 11%5Ex + 11%5E%28x%2B1%29


3%5Ex%2A%281%2B3%29 = 11%5Ex%2A%281%2B11%29


4%2A3%5Ex = 12%2A11%5Ex


3%5Ex%2F11%5Ex = 12%2F4


%283%2F11%29%5Ex = 3


Take logarithm base 3 of both sides


x%2Alog%283%2C%283%2F11%29%29 = log%283%2C%283%29%29


x%2A%281-log%283%2C%2811%29%29%29 = 1


x = 1%2F%281-log%283%2C%2811%29%29%29.      ANSWER


Solved.