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Real Values Crossed Four Power Puzzle (Posted on 2024-05-05) Difficulty: 3 of 5
Find all possible real values of x that satisfy this equation:
xx = 4x+4

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution logarithmically | Comment 1 of 4
fplot(@(x)x*log(x)-(x+4)*log(4))
grid
for x=-100:10
  % disp([x x^x 4^(x+4) x^x-4^(x+4)])
  fprintf('%5d %12d %14d %14d\n',x,x^x, 4^(x+4), x^x-4^(x+4) )
end

finds only 8 as a solution for positive integers, shown on the graph.

For negative numbers, only integers would do and none of them lead to a solution.

  Posted by Charlie on 2024-05-05 09:35:40
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