Question

3*4^x-3^x+1/2=2^2x
Решите уравнение

Answer 1

$3*4^{(x)}-3^{(x+frac{1}{2})}=2^{(2x)} \ 3*4^{(x)}-3^{(x+frac{1}{2})}=4^{(x)} \ \ 3*4^{(x)}-4^{(x)}=3^{(x+frac{1}{2})} \ (3-1)*4^{(x)}=3^{(x)}*3^{(frac{1}{2})} \ 2*4^{(x)}=3^{(x)}* sqrt{3}(|:3^{(x)}and|: 2) \ frac{4^{(x)}}{3^{(x)}} = frac{sqrt{3}}{2} \ (frac{4}{3})^{(x)} = (frac{2}{sqrt{3}})^{(-1)} \ (frac{2}{sqrt{3}})^{(2x)} = (frac{2}{sqrt{3}})^{(-1)} \ \ 2x=-1 \ x=- frac{1}{2}$