If ₂ (9^ x-1 +7 )- ₂ (3^ x-1 +1 )=2 , then x values are

Step-by-step solution

₂ (9^ x-1 +7 )- ₂ (3^ x-1 +1 )=2 ₂ ( 9^ x-1 +7 3^ x-1 +1 )=2 ₂ 2 ₂ ( 9^ x-1 +7 3^ x-1 +1 )= ₂ 2² ( 9^ x-1 +7 3^ x-1 +1 )=4 (3² )^ x-1 +7 (3^ x-1 +1 ) =4 (3^ x-1 )²+7 3^ x-1 +1 =4 Let 3^ x -1 = y y²+7 y+1 =4 y ²+7=4 y +4 y²-4 y+3=0 y²-3 y-y+3=0 y(y-3)-1(y-3)=0 ( y -3)( y -1)=0 y=3,1 If y=3 , then 3^ x-1 =3 x-1=1 x=2 If y =1 , then 3^ x-1 =3⁰ x-1=0 x=1 x=1,2