Answer: Using the logarithmic identity that says "log base b of a + log base b of c = log base b of (a*c)," we can simplify the given equation as follows:
log₂ (3x) + 4 log₁₂ (3) = log₂ (3x) + log₁₂ (3⁴) = log₂ (3x) + log₁₂ (81) = 0
Since the sum of the logarithms is equal to zero, we can write:
log₂ (3x) + log₁₂ (81) = log₂ [(3x) × 12²] = 0
Now we can solve for x:
log₂ [(3x) × 12²] = 0
(3x) × 12² = 2⁰
(3x) × 144 = 1
3x = 1/144
x = 1/144 ÷ 3
x = 1/432
Therefore, the solution for x is x = 1/432.
Explanation: