Solve:

1^x+2^x=4^x

Check your result.

(In reply to Solution by Larry)

The reason ln(1/2 - 5^(1/2)/2)/ln(2) is ruled out is that there's no such thing as a "Gaussian irrational"; i.e., a complex or imaginary number is never considered irrational. But its value does satisfy the equation; it's about -0.694241913630617 + 4.53236014182719 i and gives the LHS and RHS as  2-phi  ≈0.38196601125010515179.

Edited on March 30, 2023, 10:27 am

Posted by Charlie on 2023-03-30 10:22:57