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In the expression log_a(b) + log_a(c), what can it be simplified to?

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Question: In the expression log_a(b) + log_a(c), what can it be simplified to?

Options:

  1. log_a(bc)
  2. log_a(b/c)
  3. log_a(b-c)
  4. log_a(b+c)

Correct Answer: log_a(bc)

Solution: 

The property of logarithms states that the sum of logarithms with the same base is equal to the logarithm of the product, thus log_a(b) + log_a(c) = log_a(bc).

In the expression log_a(b) + log_a(c), what can it be simplified to?

Practice Questions

Q1
In the expression log_a(b) + log_a(c), what can it be simplified to?
  1. log_a(bc)
  2. log_a(b/c)
  3. log_a(b-c)
  4. log_a(b+c)

Questions & Step-by-Step Solutions

In the expression log_a(b) + log_a(c), what can it be simplified to?
  • Step 1: Identify the logarithmic expression you have, which is log_a(b) + log_a(c).
  • Step 2: Recognize that both logarithms have the same base, which is 'a'.
  • Step 3: Recall the property of logarithms that states: log_a(x) + log_a(y) = log_a(x * y).
  • Step 4: Apply this property to your expression: log_a(b) + log_a(c) becomes log_a(b * c).
  • Step 5: Write the final simplified expression: log_a(bc).
  • Logarithmic Properties – Understanding the properties of logarithms, specifically the property that states the sum of logarithms with the same base equals the logarithm of the product.
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