Question

sabendo que 4^x-4^x-1=24 então x^1/2 vale:

Answer 1

$4^x-4^{x-1}=24\\ 4^{x+1}(4^{-1}-4^{-2})=4\times 6\\ 4^x(\frac{1}{4}-\frac{1}{16{}x-2})=6\\ 4^x(\frac{3}{16})=6\\ 4^x(\frac{1}{16})=2\\ 4^x(4^{-2})=2\\ 4^{x-2}=2\\ (2^2)^{x-2}=2^1\\ 2^{2x-4}=2^1\\ 2x-4=1\\ 2x=5\\ x=\frac{5}{2}\\ \boxed{(\frac{5}{2})^{\frac{1}{2}}=\sqrt{\frac{5}{2}}=\frac{\sqrt{10}}{2}}$