Solve:

1^x+2^x=4^x

Check your result.

let u = 2^x
u^2 - u - 1 = 0
u = (1 ± √5)/2
But since u = 2^x must be positive, the "minus" version is rejected ("check your result").

x = log to the base 2 of (1 + √5)/2
or
x = ln((1 + √5)/2) / ln(2)
or
x = (ln(1 + √5) - ln(2)) / ln(2)

Posted by Larry on 2023-03-30 09:38:16