Question

Помогите алгебра 10 класс!!!

Answer 1

$2^{5x-4} =16^{x+3}\\2^{5x-4}=( 2^{4})^{x+3}}\\2^{5x-4}= 2^{4x+12}\\5x-4=4x+12\\x=16$

$2)3^{2x}-2* 3^{x}-3=0\\3^{x}=m>0\m^{2}-2m-3=0\D=(-2)^{2}-4*(-3)=4+12=16= 4^{2}\\m_{1}= frac{2+4}{2}=3\\m_{2} = frac{2-4}{2}=-1\\3^{x}=3\\x=1$

$3)(frac{1}{3}) ^{frac{x-1}{x-4}}=9 ^{frac{x-4}{x+4}} \\3^{frac{x-4}{x-1}}=3 ^{frac{2x-8}{x+4}}\\frac{x-4}{x-1}= frac{2x-8}{x+4}\\frac{x-4}{x-1}- frac{2x-8}{x+4}=0\\frac{x^{2}-16-2x^{2}+8x+2x-8}{(x-1)(x+4)}=0\\x-1neq0;x+4 neq0\\xneq1;x neq-4;xneq4\\-x^{2}+10x-24=0\\x^{2} -10x+24=0\\D=(-10) ^{2}-4*24=100-96=4= 2^{2}\\x_{1}= frac{10+2}{2}=6\\x_{2}= frac{10-2}{2}=4$

Ответ : 6