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If a^x = b^y and a = b, what can be inferred about x and y?
If a^x = b^y and a = b, what can be inferred about x and y?
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Practice Questions
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Q1
If a^x = b^y and a = b, what can be inferred about x and y?
x = y
x > y
x < y
x and y are unrelated
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If a = b, then a^x = b^y implies x must equal y for the equality to hold.
Questions & Step-by-step Solutions
1 item
Q
Q: If a^x = b^y and a = b, what can be inferred about x and y?
Solution:
If a = b, then a^x = b^y implies x must equal y for the equality to hold.
Steps: 5
Show Steps
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.
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