SOLUTION: Can anyone please help me with a few questions? 81^3x-3=729^x+2 find the solution set

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Question 1009511: Can anyone please help me with a few questions?
81^3x-3=729^x+2 find the solution set
Found 2 solutions by MathLover1, fractalier:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

81%5E%283x-3%29=729%5E%28x%2B2%29
%289%5E2%29%5E%283x-3%29=%289%5E3%29%5E%28x%2B2%29
9%5E%286x-6%29=9%5E%283x%2B6%29........if bases same, exponents are same too
6x-6=3x%2B6
6x-3x=6%2B6
3x=12
x=4

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From
81^(3x-3)=729^(x+2)
we change to powers of nine and get
9^2^(3x-3) = 9^3^(x+2)
9^(6x - 6) = 9^(3x + 6)
If the bases are equal, the exponents are too, so we get
6x - 6 = 3x + 6
3x = 12
x = 4