9^z - 4 x 3^z + 3 = 0?

Question

solve for z.

Answer 1

9^z - 4 x 3^z + 3 = 0

let 3^z = x

x^2-4x+3 = 0

x^2-3x-x+3 = 0

x(x-3)-1(x-3) = 0

x=3 & 1

as x=3,

3^z=3

3^z=3^1

z=1

as x=1

3^z = 1

3^z = 3^0

z = 0

Answer 2

Let 3^z = x
=> x^2 - 4x + 3 = 0
=> (x - 3)(x - 1) = 0
=> x = 3 or x = 1
=> 3^z = 3 or 3^z = 1
=> z = 1 or z = 0

Answer 3

let 3^z=t

t^2-4t+3=0
t1=1
t2=3

3^z=1=3^0
z=0

3^z=3^1
z=1