What would be the roots of the equation 4^x - 3.2^(x+2) + 32 = 0

Question

Please share all the roots and share your working also?

Answer 1

We will solve it by trial and error
X = 10,5 4^10,5 = 2097152 3,2^12,5= 2062408 difference greater than -32
X = 10,4 4^10,4 = 1825676 3,2^12,4= 1835945 same
X = 10,425 4^10,425 = 1890059 3,2^12,425 = 1890116 difference = - 57

Therefore X = 10,425 is a good solution

Comments

That's a big number!

Answer 2

Rewrite 4^x as 2^(2x), so we can rewrite the whole eq as

2^(2x) - 3 * [2^(x) * 2^2] + 32 = 0
2^(2x) - 12 * 2^(x) + 32 = 0

Let's give 2^x as y so
y^2 - 12y + 32 = 0

Factor it out:
(y - 8)(y - 4) = 0

so
y = 4, 8

Now substitute 2^x back for y and solve for each:
2^x = 4
x = 2

2^x = 8
x = 3

Hence
x = 2, 3

Answer 3

X=2,3
**if 2^x=4 if 2^x=8, X=3
X=2