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I want to solve the exponential inequality $$8^x +18^x -2\cdot 27^x>0.$$ I tried

Solve[8^x + 18^x - 2*27^x > 0, x]

and

Reduce[8^x + 18^x - 2*27^x > 0, x]

How do I tell Mathematica to do that?

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"I tried...", but you don't say what's wrong with the outcome. –  Federico Russo Jan 15 '13 at 8:40
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1 Answer

up vote 5 down vote accepted
Reduce[8^x + 18^x - 2 27^x > 0, x, Reals]
(*
 x<0
*)

Verifying

Plot[8^x + 18^x - 2*27^x, {x, -6, 3/2}]

Mathematica graphics

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Thank you very much. –  minthao_2011 Oct 27 '12 at 2:58
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