Question

4 elevado a x+1 menos 12 e igual a 2 elevado a x+1

Answer 1

Olá, tudo bem?

$4^{x+1}-12=2^{x+1}\to 4^{x+1}-2^{x+1}-12=0\to\\\\\left(2^{x+1}\right)^{2}-2^{x+1}-12=0\to \text{Fazendo}\,\,\left(2^{x+1}\right)=k,\,\,\text{teremos:}\\\\k^{2}-k-12=0\to\text{Bhaskara}\to\\\\k=\dfrac{-(-1)\pm\sqrt{(-1)^2-4\times 1\times (-12)}}{2\times 1}\to k=\dfrac{1\pm7}{2}\\\\\text{Para}\,\,k=-3\to2^{x+1}=-3\,\,\text{imposs\'ivel}\\\\\text{Para}\,\,k=4\to 2^{x+1}=4\to 2^{x+1}=2^2\to x+1=2\to\boxed{x=1}$

É isso!! :)