If log₃ (x − 2) + log₃ (x + 4) = 2, then x equals:

Explanation

Combine: log₃[(x−2)(x+4)] = 2, so (x−2)(x+4) = 9, giving x² + 2x − 8 = 9, x² + 2x − 17 = 0. That does not factor nicely, so check the data: this gives x = −1 ± √18, and the only valid root is −1 + 3√2 ≈ 3.24, which is not an option. Hence recompute with the stated options: for x = 3, (1)(7) = 7, not 9.

More Ratio and Proportion, Indices and Logarithms questions

• The monthly wages of 12 workers at a factory in Pune total ₹1,80,000. A contractor wants to hire 18 workers on the same pay basis per worker…
• If 6, x and 24 are in continued proportion with x positive, and the third proportional to 6 and x is y, what is the value of x + y?
• If x = 4ab/(a + b), with a ≠ b and a, b ≠ 0, then the value of (x + 2a)/(x − 2a) + (x + 2b)/(x − 2b) is:
• The value of (log₂ 9) × (log₃ 8) is:
• Given log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4771, the value of log₁₀ 72 is:
• If the sub-duplicate ratio of x : 25 is equal to 3 : 5, then x equals: