Given that y= 2* (power of x)
a) express 4*(power of x) in terms of y
b) hence, or otherwise solve
8(4*) - 9(2*) + 1 = 0

A)
y=2^x

4^x=2^(2x)=y²

solution:
y=2^x hence y²=4^x

chek:
x=5 ⇒ y=2⁵=32
4⁵=1024
y₂=32²=1024

b)
 8(4^x)-9(2^x)+1=0
8(2^(2x)-9(2^x)+1=0

2^x=t

8t²-9t+1=0
We solve the quadratic.
t₁=1/8    ⇒2^x=1/8
2^x=1/2³
2^x=2⁻³
x=-3

t₂=1  ⇒ 2^x=1  ⇒x=0

Solutions:
x=-3
x=0