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If log_3(x) + log_3(4) = 2, find x.

Practice Questions

Q1
If log_3(x) + log_3(4) = 2, find x.
  1. 1
  2. 4
  3. 9
  4. 12

Questions & Step-by-Step Solutions

If log_3(x) + log_3(4) = 2, find x.
Correct Answer: 2.25
  • Step 1: Start with the equation log_3(x) + log_3(4) = 2.
  • Step 2: Use the property of logarithms that says log_a(b) + log_a(c) = log_a(b*c).
  • Step 3: Combine the logs: log_3(x * 4) = 2.
  • Step 4: Rewrite the equation in exponential form: x * 4 = 3^2.
  • Step 5: Calculate 3^2, which is 9: x * 4 = 9.
  • Step 6: Solve for x by dividing both sides by 4: x = 9 / 4.
  • Step 7: Simplify 9 / 4 to get x = 2.25.
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