Не могу решить задачу
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log(8) ( x + y) + log(8) ( x - y) = 1 1/3

одз  x + y > 0   x - y > 0

log(8) (x + y)(x - y) = log(8) 8^4/3

(x + y)(x - y) = 16

6^(1 + log(4) ( x + y)) = 48

6*6^log(2) √(x + y) = 6*8

x ^ log(y) z = y^ log(x) z

2^log(6) √(x + y) = 2^3

log(6) √(x + y) = 3

√(x + y) = 6^3

x + y = 6^6

x - y = 16/6^6

2x = 6^6 + 16/6^6

x = (6^6 + 16/6^6)/2

y = (6^6 - 16/6^6)/2

Відповідь:

x=4.099494563

y=0.8976946457

Покрокове пояснення:

log_8 (x+y)+log_8 (x-y) = 1/3log_2 (x+y)+1/3log_2 (x-y)=4/3

log_2 (x+y)+log_2 (x-y)=4

log(x^2-y^2)=log_2(2^4)

x^2-y^2=16

6^(log_4(x+y)=8

(6^(log_2(x+y))^(1/2)=8

6^(log_2(x+y)=64

log_6(6^(log_2(x+y)) =log_6 (64)

log_2(x+y)=6/log_2(6)=2.3211168434

Подставим в предидущее уравнение

log_2 (x+y)+log_2 (x-y)=4

log_2 (x-y)=4-2.3211168434=1.678883156

x-y=2^1.678883156

x-y=3.201799918

x=y+3.201799918

Подставим x в

x^2-y^2=16

(y+3.201799918)^2-y^2=6.403599836y+10.251522714=16

y=0.8976946457

Подставим y в x=y+3.201799918

x=0.8976946457+3.201799918

x=4.099494563