Question

математика математика математика ​

Answer 1

$\hspace{-1,4em}6) ~~ 0,5^{5-2x} + 3 \cdot 0,25^{3-x} = 5 \\\\ (2^{-1})^{5-2x} + 3\cdot (2^{-2})^{3-x} = 5 \\\\ 2 ^{2x}\cdot \dfrac{1}{32} + 2^{2x} \cdot \dfrac{3}{64} = 5 ~ \big | \cdot 64 \\\\ 5 \cdot 2^{2x} = 64 \cdot 5 \\\\ 2^{2x} = 64 \\\\ 2x = 6 \\\\ x = 3$

$\displaystyle \hspace{-1,4em}7) ~~ 2^{2x+1} + 4^x - \bigg (\frac{1}{16} \bigg )^{1-0,5x}\!\!\!= 47 \\\\ 2\cdot 2^{2x} + 2^{2x} - 2^{- 4 + 2x} = 47 \\\\ 3\cdot 2^{2x} -\frac{1}{16}\cdot 2^{2x} = 47 ~ \\\\ 2^{2x}\bigg(3-\frac{1}{16} \bigg )= 47 \\\\ 2^{2x} \cdot \frac{47}{16} = 47 \\\\ 2^{2x}= 16 \\\\ 2x = 4 \\\\ x = 2$

$\displaystyle \hspace{-1,4em}8) ~~ 4 \cdot 3^x - 5\cdot 3^{x-1}- 6 \cdot 3^{x-2}= 15 \cdot 9^{x^2-1} \\\\\ 4\cdot 3^x - \frac{5}{3}\cdot 3^x - \frac{2}{3}\cdot 3^x = \frac{5}{3} \cdot 3^{2x^2} \\\\ 3^x \bigg(4-\frac{5}{3}-\frac{2}{3} \bigg) = \frac{5}{3}\cdot 3^{2x^2} \\\\ 3^x \cdot \frac{5}{3}= \frac{5}{3} \cdot 3^{2x^2} \\\\ 3^{2x^2}= 3^x ~ \big |: 3^x \\\\ 3^{2x^2-x} = 3^0 \\\\ 2x^2 - x =0 \\\\ x_1 = 0 ~~ ; ~~ x_2 = \frac{1}{2}$