How to solve this exponential inequality?

Question

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?

belisarius · Accepted Answer · 2012-10-27 02:56:36Z

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

answered Oct 27 '12 at 2:56

belisarius
29.9k347121

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

1 Answer