3x+1 + 32x+1 = 270
Use the principle that 
on each term on the left:
3x·31 + 32x·31 = 270
3x·3 + 32x·3 = 270
Divide through by 3
3x + 32x = 90
Rearrange the equation with 0 on the right:
32x + 3x - 90 = 0
Let u = 3x
Then u² = 32x
u² + u - 90 = 0
(u - 9)(u + 10) = 0
u - 9 = 0; u + 10 = 0
u = 9 u = -10
Using u = 9
Since u = 3x
3x = 9
Write 9 as 3²
3x = 3²
Since the base 3 is the same on both
sides, is positive and not 1, we can
equate the exponents:
x = 2
Using u = -10
Since u = 3x
3x = -10
Since all powers of 3 are positive,
and -10 is negative, there is no
solution to this part, and so u=-10
is extraneous.
Therefore x=2 is the only solution.
Edwin
