If log318 + log33 - log3x = 3, Find x.

Analyze the question: We have log₃18 + log₃3 − log₃x = 3 and need to find x.

Concept: Log laws (same base):

• log a + log b = log(ab)
• log a − log b = log(a/b)
• log_b(N) = k means N = b^k

Solution:

1. Combine the logs: log₃(18 × 3 / x) = 3 log₃(54/x) = 3

2. Convert to index form: 54/x = 3³ = 27

3. Solve for x: x = 54/27 = 2

Check: log₃18 + log₃3 − log₃2 = log₃(54/2) = log₃27 = 3 ✓

Answer: x = 2, which is option B.

Tip: When you see several logs with the same base, first combine them into a single log (add → multiply, subtract → divide), then switch to index form. Also remember that 3³ = 27, which is a common value in JAMB questions.