Question

Solve for x:

log_x4 = 2 – log_x9

Answer 1

We are given:

log_x4 = 2 – log_x9

Step 1: Move all log terms to one side

log_x4 + log_x9 = 2

Use the product rule:

log_x(4 · 9) = log_x36

So:

log_x36 = 2

Step 2: Convert to exponential form

x² = 36

⇒ x = ±6

Step 3: Check validity

• Logarithms are only defined for positive bases ≠ 1, so:
  • x = 6 → valid
  • x = – 6 → invalid

x = 6