Question

Помогите алгебра 10 класс!!!

Answer 1

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

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

$3)(\frac{1}{3}) ^{\frac{x-1}{x-4}}=9 ^{\frac{x-4}{x+4}} \\\\3^{\frac{x-4}{x-1}}=3 ^{\frac{2x-8}{x+4}}\\\\\frac{x-4}{x-1}= \frac{2x-8}{x+4}\\\\\frac{x-4}{x-1}- \frac{2x-8}{x+4}=0\\\\\frac{x^{2}-16-2x^{2}+8x+2x-8}{(x-1)(x+4)}=0\\\\x-1\neq0;x+4 \neq0\\\\x\neq1;x \neq-4;x\neq4\\\\-x^{2}+10x-24=0\\\\x^{2} -10x+24=0\\\\D=(-10) ^{2}-4*24=100-96=4= 2^{2}\\\\x_{1}= \frac{10+2}{2}=6\\\\x_{2}= \frac{10-2}{2}=4$

Ответ : 6