Question

Помогите пожалуйста 9 класс​

Answer 1

$1)\sqrt{2}=16^{x}\\\\2^{\frac{1}{2}}=2^{4x}\\\\\frac{1}{2}=4x\\\\x=\frac{1}{8}\\\\Otvet:\boxed{\frac{1}{8}}$

$2)25^{2x+3}=5^{-3x-1}\\\\(5^{2})^{2x+3}=5^{-3x-1}\\\\5^{4x+6}=5^{-3x-1}\\\\4x+6=-3x-1\\\\4x+3x=-1-6\\\\7x=-7\\\\x=-1\\\\Otvet:\boxed{-1}$

$3)(\frac{1}{9})^{2x-5}=3^{5x-8}\\\\(3^{-2})^{2x-5}=3^{5x-8}\\\\3^{-4x+10} =3^{5x-8}\\\\-4x+10=5x-8\\\\-4x-5x=-8-10\\\\-9x=-18\\\\x=2\\\\Otvet:\boxed{2}$

$4)\frac{25^{x-2}}{\sqrt{5}}=1\\\\\frac{(5^{2})^{x-2}}{5^{\frac{1}{2}}}=1\\\\\frac{5^{2x-4}}{5^{0,5}}=1\\\\5^{2x-4-0,5}=1\\\\5^{2x-4,5}=5^{o}\\\\2x-4,5=0\\\\2x=4,5\\\\x=2,25=2\frac{1}{4}\\\\Otvet:\boxed{2\frac{1}{4}}$

$5)\frac{8}{(\sqrt{2})^{x}}=4^{3x-2}*\sqrt{2}\\\\\frac{2^{3}}{2^{0,5x}}=(2^{2})^{3x-2}*2^{0,5} \\\\2^{3-0,5x}=2^{6x-4+0,5}\\\\3-0,5x=6x-3,5\\\\-0,5x-6x=-3,5-3\\\\-6,5x=-6,5\\\\x=1\\\\Otvet:\boxed{1}$

$6)49^{0,5x-\frac{1}{2}} =1\\\\ 49^{0,5x-0,5}=49^{o}\\\\0,5x-0,5=0\\\\0,5x=0,5\\\\x=1\\\\Otvet:\boxed{1}$