Question

solve for x 3^(x+1) +3^(2x+1) = 270

Answer 1

Answer: x=2

Step-by-step explanation:

3^(x+1) +3^(2x+1) = 270

3^x ×3+3^2x×3 = 270

Divide by 3 both sides

3^x + 3^2x= 90, 3^x + (3^x)2= 90

Put, 3^x= Y

So, y+y^2= 90

y^2+y -90= 0.

y^2 +10y-9y-90=0

y(y+10) -9(y+10) =0

(y+10) (y-9) 0

So, y= 9 or y= 10

But 3^x= y,

So, 3^x= 9=3^2, x=2,

Or, 3^x= 10, not possible.