Дано

$$frac{log{left (x + 2 y right )}}{log{left (7 right )}} = 1$$

3*x + 5 x + y
4 = 16

$$4^{3 x + 5} = 16^{x + y}$$
Ответ
$$x_{1} = 1$$
=
$$1$$
=

1

$$y_{1} = 3$$
=
$$3$$
=

3

$$x_{2} = 1 – frac{2 i pi}{log{left (2 right )}}$$
=
$$1 – frac{2 i pi}{log{left (2 right )}}$$
=

1 – 9.06472028365439*i

$$y_{2} = frac{log{left (8 right )} + i pi}{log{left (2 right )}}$$
=
$$frac{log{left (8 right )} + i pi}{log{left (2 right )}}$$
=

3 + 4.53236014182719*i

$$x_{3} = 1 – frac{i pi}{log{left (2 right )}}$$
=
$$1 – frac{i pi}{log{left (2 right )}}$$
=

1 – 4.53236014182719*i

$$y_{3} = frac{log{left (64 right )} + i pi}{2 log{left (2 right )}}$$
=
$$frac{log{left (64 right )} + i pi}{2 log{left (2 right )}}$$
=

3 + 2.2661800709136*i

$$x_{4} = 1 + frac{i pi}{log{left (2 right )}}$$
=
$$1 + frac{i pi}{log{left (2 right )}}$$
=

1 + 4.53236014182719*i

$$y_{4} = frac{log{left (64 right )} – i pi}{2 log{left (2 right )}}$$
=
$$frac{log{left (64 right )} – i pi}{2 log{left (2 right )}}$$
=

3 – 2.2661800709136*i

$$x_{5} = 2 – frac{2 log{left (-1 – i right )}}{log{left (2 right )}}$$
=
$$2 – frac{2 log{left (-1 – i right )}}{log{left (2 right )}}$$
=

1 + 6.79854021274079*i

$$y_{5} = frac{5}{2} + frac{log{left (-1 – i right )}}{log{left (2 right )}}$$
=
$$frac{1}{log{left (2 right )}} left(frac{1}{2} log{left (32 right )} + log{left (-1 – i right )}right)$$
=

3 – 3.3992701063704*i

$$x_{6} = 2 – frac{2 log{left (-1 + i right )}}{log{left (2 right )}}$$
=
$$2 – frac{2 log{left (-1 + i right )}}{log{left (2 right )}}$$
=

1 – 6.79854021274079*i

$$y_{6} = frac{5}{2} + frac{log{left (-1 + i right )}}{log{left (2 right )}}$$
=
$$frac{1}{log{left (2 right )}} left(frac{1}{2} log{left (32 right )} + log{left (-1 + i right )}right)$$
=

3 + 3.3992701063704*i

$$x_{7} = 2 – frac{2 log{left (1 – i right )}}{log{left (2 right )}}$$
=
$$2 – frac{2 log{left (1 – i right )}}{log{left (2 right )}}$$
=

1 + 2.2661800709136*i

$$y_{7} = frac{5}{2} + frac{log{left (1 – i right )}}{log{left (2 right )}}$$
=
$$frac{1}{log{left (2 right )}} left(frac{1}{2} log{left (32 right )} + log{left (1 – i right )}right)$$
=

3 – 1.1330900354568*i

$$x_{8} = 2 – frac{2 log{left (1 + i right )}}{log{left (2 right )}}$$
=
$$2 – frac{2 log{left (1 + i right )}}{log{left (2 right )}}$$
=

1 – 2.2661800709136*i

$$y_{8} = frac{5}{2} + frac{log{left (1 + i right )}}{log{left (2 right )}}$$
=
$$frac{1}{log{left (2 right )}} left(frac{1}{2} log{left (32 right )} + log{left (1 + i right )}right)$$
=

3 + 1.1330900354568*i

Численный ответ
Читайте также  a+2*b-4*c=6 3*a+5*c=7 a4+3*b=8

x1 = -49.76871161688474 – 35.46366037497679*i
y1 = 28.38435580844237 + 17.73183018748839*i

x2 = -29.84956820800321 – 0.0002208166212280573*i
y2 = 18.42478410400161 + 0.0001104083106140287*i

x3 = -31.05135561517087 + 47.12374043289246*i
y3 = 19.02567780758544 – 23.56187021644623*i

x4 = 1.00000000000000
y4 = 3.00000000000000

   
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