Solve for 3^X - 3^Y given 3^X / 3^Y = 3 and 3^X + 3^Y = 12

Published on August 26, 2024

Question

Answer

Let’s approach this problem step by step:
  1. From the first equation:
    This can be rewritten as:
    Therefore,
  2. From the second equation:
  3. Let’s use the information from step 1 to rewrite in terms of :
  4. Substituting this into the second equation:


  5. Now that we know , we can find :
  6. The third equation asks for
  7. We can now solve this:
Therefore, the answer to is 6.
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