Solve `4^x+6^x=9^xdot`

Answer

`x = log_(2//3)((sqrt(5)-1)/(2))`

Explanation

`4^(x) + 6^(x) = 9^(x)`
or `((4)/(9))^(x)+((2)/(3))^(x) = 1`
Putting `((2)/(3))^(x) = y ,` we have
`y^(2) + y - 1 = 0`
or ` y = (-1pmsqrt(5))/(2)`
`rArr ((2)/(3))^(x) = (sqrt(5-1))/(2) (because((2)/(3))^(x) gt0)`
`rArr x = log_(2//3)((sqrt(5-1))/(2)) `