Question

математика математика математика ​

Answer 1

Ответ:

3.

$2 \times {7}^{x} + {7}^{x + 2} - 3 \times {7}^{x - 1} = 354 \\ 2 \times {7}^{x} + {7}^{x} \times {7}^{2} - 3 \times {7}^{x} \div {7}^{1} = 354 \\ {7}^{x} (2 + 49 - \frac{3}{7} ) = 354 \\ {7}^{x} \times \frac{354}{7} = 354 \\ {7}^{x} = 354 \times \frac{7}{354 } \\ {7}^{x} = {7}^{1} \\ x = 1$

4.

${4}^{x - 2} - 3 \times {2}^{2x - 1} + 5 \times {2}^{2x} = 228 \\ {2}^{2x - 4} - 3 \times {2}^{2x - 1} + 5 \times {2}^{2x} = 228 \\ {2}^{2x} \div {2}^{4} - 3 \times {2}^{2x} \div {2}^{1} + 5 \times { 2}^{2x} = 228 \\ {2}^{2x} ( \frac{1}{16} - \frac{3}{2} + 5) = 228 \\ {2}^{2x} = 228 \times \frac{16}{57} \\ {2}^{2x} = 4 \times 16 \\ {2}^{2x} = {2}^{2} \times {2}^{4} \\ {2}^{2x} = {2}^{2 + 4} \\ 2x = 6 \\ x = 3$

5.

$4 \times {9}^{1.5x - 1} - {27}^{x - 1} = 33 \\ 4 \times {3}^{3x - 2} - {3}^{3x - 3} = 33 \\ 4 \times {3}^{3x} \div {3}^{2} - {3}^{3x} \div {3 }^{3} = 33 \\ {3}^{3x} ( \frac{4}{9} - \frac{1}{27} ) = 33 \\ {3}^{3x} = 33 \times \frac{27}{11} \\ {3}^{3x} = 3 \times {3}^{3} \\ {3}^{3x} = {3}^{4} \\ 3x = 4 \\ x = \frac{4}{3} \\ x = 1 \frac{1}{3}$