Question

Решить показательные уравнения.

Answer 1

$9^{x}-2^{x+0.5} = 2^{x+3.5}-3^{2x-1}\ 3^{2x}+3^{2x}/3 = 2^{x+3.5}+2^{x+0.5}\ 9^x(1+1/3) = 2^xsqrt{2}(2^3+1)\ (9/2)^x=9div4/3\ (9/2)^x = 27/(2sqrt{2}) = (9/2)^{3/2}\ x=3/2\\ 4^x-3^{x-0.5}=3^{x+0.5}-2^{2x-1}\ 4^x+4^x/2 =3^{x+0.5}+3^{x-0.5}\ 4^xcdot3/2 = 3^x(sqrt{3}+1/sqrt{3})\ (4/3)^x =frac{2}{3}(sqrt{3}+1/sqrt{3}) = frac{2}{3}frac{4}{sqrt{3}} = (4/3)^{3/2}\ x=3/2$