Question

Solve 4^x + 2^(x+2) = 8 Thanks!:)? 

Answer 1

The equation 4^x + 2^x+2 = 8

(2²)^x + 2^x 2² = 8

Apply the formula a^m + aⁿ = a^m+n

(a^m)ⁿ = a^mn

2^2x + 2^x (4) = 8

(2^x)² + 2^x (4) - 8 = 0

Let 2^x = X

Now the equation becomes X² + 4X - 8 = 0

Compare it to quadratic form

Roots are

Consider x = 1.46

2^x = 1.46

log(2^x ) = log(1.46)

x log (2) = log(1.46)

x = log(1.46)/log(2)

x = 0.5459.

Solution x = 0.5459.