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If a^x = b^y, then log_a(b) is equal to?

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Question: If a^x = b^y, then log_a(b) is equal to?

Options:

  1. y/x
  2. x/y
  3. x+y
  4. y-x

Correct Answer: y/x

Solution: 

From a^x = b^y, taking log_a on both sides gives log_a(b^y) = x, hence y * log_a(b) = x, thus log_a(b) = y/x.

If a^x = b^y, then log_a(b) is equal to?

Practice Questions

Q1
If a^x = b^y, then log_a(b) is equal to?
  1. y/x
  2. x/y
  3. x+y
  4. y-x

Questions & Step-by-Step Solutions

If a^x = b^y, then log_a(b) is equal to?
  • Step 1: Start with the equation a^x = b^y.
  • Step 2: Take the logarithm base a of both sides of the equation. This gives us log_a(a^x) = log_a(b^y).
  • Step 3: Use the property of logarithms that states log_a(a^x) = x. So, we have x = log_a(b^y).
  • Step 4: Apply the power rule of logarithms, which states log_a(b^y) = y * log_a(b). Now we have x = y * log_a(b).
  • Step 5: To find log_a(b), rearrange the equation: log_a(b) = x / y.
  • Logarithmic Properties – Understanding how to manipulate logarithmic equations and apply the change of base formula.
  • Exponential Equations – Recognizing the relationship between exponential forms and logarithmic forms.
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