Problems need HardWork #22

Algebra Level 2

Find the sum of all real $x$ satisfying the equation :

$2^x + 3^x - 4^x + 6^x - 9^x = 1$

1 solution

Dev Sharma
Aug 28, 2015

Let $2^x = a$ and $3^x = b$ , multiply both sides of the equation by $2$ and completing the squares gives :

$(1 - a)^2 + (a - b)^2 + (b - 1)^2 = 0$

It gives $1 = 2^x = 3^x$ and $x = 0$ is the only solution.