Question

Solve for x 4^x2 / 4^2x + 3 = 1

Answer 1

I read this as 4^(x^2)/(4^(2x+3))=1

4^(x^2)=4^(2x+3)

Equating exponents: x^2=2x+3, x^2-2x-3=0=(x-3)(x+1), so x=3 or -1.

CHECK

4^(-1)^2/4^(-2+3)=4/4=1 OK

4^9/4^(6+3)=4^9/4^9=1 OK

Answer 2

Solve for x 4^x2 / 4^2x + 3 = 1

I think there should be some brackets in your expression which would make it look like this,

4^(x^2) / (4^(2x + 3)) = 1

Now we simply subtract the exponent of the term in the denominator from that of the numerator, to give

4^(x^2 - 2x - 3) = 1

Therefore, x^2 - 2x - 3 = 0

factorising gives us,

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

Therefore, x = 3, or x = -1