If 2 log x (3$\frac{3}{8}$) = 6, find the value of x

Analyze the question: "2 log x (3 3/8) = 6" is read as 2 log base x of (3 3/8) = 6. That means log base x of (27/8) = 3.

Concept: If log_x(N) = k, then x^k = N.

Solution:

1. Convert the mixed number: 3 3/8 = 27/8.
2. Divide both sides by 2: log_x(27/8) = 3.
3. Rewrite in index form: x³ = 27/8.
4. Take the cube root: x = ∛27 / ∛8 = 3/2.

Check: (3/2)³ = 27/8 = 3 3/8, so 2 × 3 = 6 ✓.

The answer is x = 3/2, which is option A.

Tip: When you see "log base x of N = k", immediately convert to x^k = N. Learn the common cubes (8, 27, 64, 125) so you can take cube roots of fractions quickly.