2^(x-2)-2^(x-1)+2^x=24

Question

2^(x-2)-2^(x-1)+2^x=24

Answer 1

2^x/4-2^x/2+2^x=24

2^x=t

t/4-t/2+t=24

t(1-1/2+1/4)=24

t*3/4=24

t=24*4/3=32

2^x=32

x=5

Answer 2

2^(x-2)-2^(x-1)+2^x=24

 

2^x*(1/4) - 2^x*(1/2) + 2^x = 24

 

2^x*(1/4-1/2+1) = 24

 

2^x * (3/4) = 24

 

2^x = 32

 

2^x= 2^5 ⇒ x=5