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If a^x = b^y and a = b, what can be inferred about x and y?

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Question: If a^x = b^y and a = b, what can be inferred about x and y?

Options:

  1. x = y
  2. x > y
  3. x < y
  4. x and y are unrelated

Correct Answer: x = y

Solution: 

If a = b, then a^x = b^y implies x must equal y for the equality to hold.

If a^x = b^y and a = b, what can be inferred about x and y?

Practice Questions

Q1
If a^x = b^y and a = b, what can be inferred about x and y?
  1. x = y
  2. x > y
  3. x < y
  4. x and y are unrelated

Questions & Step-by-Step Solutions

If a^x = b^y and a = b, what can be inferred about x and y?
  • Step 1: Start with the equation a^x = b^y.
  • Step 2: Note that we are given that a = b.
  • Step 3: Substitute b with a in the equation: a^x = a^y.
  • Step 4: Since the bases (a) are the same, the exponents must be equal for the equation to hold true.
  • Step 5: Therefore, we can conclude that x must equal y.
  • Exponential Equations – Understanding the properties of exponents and how they relate when the bases are equal.
  • Equality of Exponents – Recognizing that if two exponential expressions with the same base are equal, their exponents must also be equal.
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