Question

Решите уравнения :
1)7¹²: (2x - 3) = 7⁸
2) 4¹⁶ : (0,1x+ 1,3) = 4¹⁰
3) 3³ * (191- 2x) = 3⁶
4) 25²* (10x +6,1) = 25⁴​

Answer 1

Пошаговое объяснение:

$1) \: \dfrac{ {7}^{12} }{2x - 3} = {7}^{8} \\ {7}^{12} = {7}^{8} (2x - 3) \: ( \div \: {7}^{8} ) \\ 2x - 3 = {7}^{4} \\ 2x = 2401 + 3 \\ 2x = 2404 \\ x = \dfrac{2404}{2} \\ x = 1202.$

$2) \: \dfrac{ {4}^{16} }{0.1x + 1.3} = {4}^{10} \\ {4}^{16} = {4}^{10} (0.1x + 1.3) \: ( \div \: {4}^{10} )\\ 0.1x + 1.3 = {4}^{6} \\ 0.1x = 4096 - 1.3 \\ 0.1x = 4094.7 \\ x = \frac{4094.7}{0.1} \\ x = 40947.$

$3) \: {3}^{3} (191 - 2x) = {3}^{6} \: ( \div \: {3}^{3} ) \\ 191 - 2x = {3}^{3} \\ - 2x = 27 - 191 \\ - 2x = - 164 \\ x = \dfrac{ - 164}{ - 2} \\ x = 82.$

$4) \: {25}^{2} (10x + 6.1) = {25}^{4} \: ( \div \: 25 {}^{2} ) \\ 10x + 6.1 = 25 {}^{2} \\ 10x = 625 - 6.1 \\ 10x = 618.9 \\ x = \frac{618.9}{10} \\ x = 61.89.$