1 is a solution, and, to put it another way,
2^x + 3^x + 6^x  x^2 = 0, for x = 1
The function on the LHS has derivative
ln(2)2^x + ln(3)3^x+ln(6)6^x  2x
which, at x=1, equals approximately 3.011404264707352, which is positive, and in fact is everywhere positive, as can be seen by graphing, so x=1 is the only solution.

Posted by Charlie
on 20151027 16:00:01 