Question

12 задание с логорифмами

Answer 1

log₂₊ₓ 3 + 2/log₂ (2 + x) = 1

log₂₊ₓ 3 + 2 log₂₊ₓ 2 = 1

log₂₊ₓ 3 + log₂₊ₓ 4 = 1

log₂₊ₓ (3·4) = 1

(2 + x)¹ = 12

x = 10

Answer 2

$log_{2 + x}( 3 ) + \frac{2}{ log_{2}(2 + x) } = 1 \\ odz \\ 2 + x > 0 \: \: \: x > - 2 \\ 2 + x≠1 \: \: \: x ≠ - 1 \\ log_{2}(2 + x) ≠ 0 \\ 2 + x = 1 \\ x ≠ - 1 \\ x∈\: ( - 2;- 1)(-1;+ ∞) \\ log_{2 + x}(3) + \frac{2}{ \frac{1}{ log_{2 + x}(2) } } = 1 \\ log_{2 + x}(3) + 2 log_{2 + x}(2) = 1 \\ log_{2 + x}(3) + log_{2 + x}(4) = 1 \\ log_{2 + x}(12) = 1 \\ 2 + x = 12 \\ x = 10$