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.
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; +∞)
--------------------------
ответ: 6.