1/2 log2 (x-2)^2+1/3 log2(x-4)^3=3​

log(a^k) b^b = b/k log(a) b

log a + log b = log ab

1/2 log2 (x-2)^2+1/3 log2(x-4)^3=3​

одз x ≠ 2   x>4

1/2 *2  log2 (x-2)+1/3 *3  log2(x-4) = 3​

log2 (x-2) + log2(x-4) = 3​

log2 (x-2)(x-4) = 3​

(x-2)(x-4) = 8

​x^2 - 2x - 4x + 8 = 8

​x(x - 6) = 0

x = 0 не проходит по одз

x = 6

ОДЗ:

x ∈ (4; +∞)

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ответ: 6.