8^x -3*4^x+1 -2^x+2 +48=0. Created by GUz0. algebra-ru

8^x -3*4^x+1 -2^x+2 +48=0...

Evgenia4836

Verified answer

$8^x-3*4^{x+1}-2^{x+2}+48=0$

$8^x-3*4*4^x-4*2^x+48=0$

$2^{3x}-12*2^{2x}-4*2^x+48=0$

$2^x(2^{2x}-4)-12(2^{2x}-4)=0$

$(2^x-12)*(4^x-4)=0\\x1=1\\x2=log2(12)$

2 votes Thanks 2

NNNLLL54

Verified answer

$8^{x}-3\cdot 4^{x+1}-2^{x+2}+48=0\\\\2^{3x}-12\cdot 2^{2x}-4\cdot 2^{x}+48=0\\\\t=2^{x}>0\; \; ,\; \; t^3-12t^2-4t+48=0\; ,\\\\(t^3-4t)-(12t^2-48)=0\\\\t\, (t^2-4)-12(t^2-4)=0\\\\(t^2-4)(t-12)=0\\\\a)\; \; t^{2}=4\; \; ,\; \; t=\pm 2\; \; \Rightarrow \; \; 2^{x}=2>0\; \; ,\; \; x=1\\\\b)\; \; t=12\; \; ,\; \; 2^{x}=12\; \; \Rightarrow \; \; x=log_212=2+log_23\\\\Otvet:\; \; x=1\; ,\; x=2+log_23\; .$

0 votes Thanks 0

Answers & Comments

Verified answer

Verified answer

sostavit pishevuyu cep lyubogo na vybor biogeocenoza i lyubogo agrocenoza

imeetsya dva splava pervyj splav soderzhit 7 olova vtoroj 14 olova massa vt96753e37e1e63958dae7f2c87ab59284 93146

рекомендуемые вопросы

Helpful Links

Helpful Social