4^a+2=3 times 2^α

Question

Solve the equation

Answer 1

4^a+2=3*2^a

(2²)^a-3*2^a+2=0

(2^a)²-3*2^a+2=0 

 This is a quadratic equation with respect to 2^a. You can make  substitution y=2^a or just solve directly.

We can factor it

(2^a-2)(2^a-1)=0

2^a-2=0 or/and 2^a-1=0

2^a=2

2^a=2¹

a=1.

Similar for

2a-1=0

2^a=1

2^a=2⁰

a=0.

So, we have two solutions (roots). Check..