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alovosiem
@alovosiem
July 2022
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tausinv
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X^(log(2)(x^3) - log(2)(x)^2 -3) = 1/x
x > 0 - ОДЗ
log(2)(x^3) - log(2)(x)^2 -3 = - 1
3*log(2)(x) - log(2)(x)^2 - 2 = 0
log(2)(x) = t
t^2 - 3*t + 2 = 0
t1 + t2 = 3
t1 * t2 = 2
t1 = 2, t2 = 1
log(2)(x) = 2
x = 2^2 = 4
log(2)(x) =1
x = 2^1 = 2
Оба решения удовлетворяют ОДЗ.
Ответ: x = 2, x = 4
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Answers & Comments
Verified answer
X^(log(2)(x^3) - log(2)(x)^2 -3) = 1/xx > 0 - ОДЗ
log(2)(x^3) - log(2)(x)^2 -3 = - 1
3*log(2)(x) - log(2)(x)^2 - 2 = 0
log(2)(x) = t
t^2 - 3*t + 2 = 0
t1 + t2 = 3
t1 * t2 = 2
t1 = 2, t2 = 1
log(2)(x) = 2
x = 2^2 = 4
log(2)(x) =1
x = 2^1 = 2
Оба решения удовлетворяют ОДЗ.
Ответ: x = 2, x = 4