Question

X=?         9^{x+2} + 9^{x+1} + 9^{x}=91x3^{28} 

Answer 1

[tex]9^{x+2}+9^{x+1}+9^x=91\cdot 3^{28}\\ 9^x\cdot9^2+9^x\cdot9^1+9^x\cdot 1=91\cdot3^{28}\\ 9^x\cdot(81+9=1)=91\cdot3^{28}\\ 9^x\cdot91=91\cdot3^{28}\\ 9^x=3^{28}\\ (3^2)^x=3^{28}\\ 3^{2x}=3^{28}\\ 2x=28\\ x=14[/tex]

Answer 2

$9^{x+2} + 9^{x+1} + 9^{x} = 91 * 3^{28}$

Dam factor comun pe 9^x

$9^{x}*( 9^{2}+ 9^{1} + 9^{0} )=91* 3^{28}$

$9^{x} *(81+9+1) = 91* 3^{28}$

$9^{x} * 91 = 91* 3^{28} <=> 9^{x} = 3^{28} <=> 3^{2x} 3^{28} <=>2x=28 =>$

$=> x= \frac{28}{2} = 14$