Expand Logarithms Worksheets

There are four sets of logarithm & exponential worksheets:

• Exponential & Logarithmic Forms
  
• Evaluate Logarithms
  
• Expand Logarithms
  
• Condense Logarithms
  

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to expand logarithms.

How to expand logarithms?

There are two sets of expanding logarithm worksheets.

• Expand Logarithms.
• Expand Logarithms (Include Radicals).

Expanding logarithms means using logarithmic properties to simplify a complex logarithmic expression into a simpler form. Here are some techniques for expanding logarithms:

1. Product Rule for Logarithms:
   The product rule for logarithms states that
   log_b(MN)=log_b(M) + log_b(N).
   This allows you to expand a logarithm when you have a product inside it.
   For example, to expand log₂(5x):
   log₂(5x) = log₂(5) + log₂(x)

2. Quotient Rule for Logarithms:
   The quotient rule for logarithms states that
   log_b(M/N) = log_b(M) - log_b(N)
   This allows you to expand a logarithm when you have a quotient inside it.
   For example, to expand log₅(8/x)
   log₅(8/x) = log₅(8) - log₅(x)

3. Power Rule for Logarithms:
   The power rule for logarithms states that
   log_b(Mⁿ) = n log_b(M)
   This allows you to move the exponent inside the logarithm as a coefficient.
   For example, to expand log₃(5²)
   log₃(5²) = 2 log₃(5)

These techniques can help you expand logarithmic expressions and simplify them into more manageable forms. It’s essential to know when and how to use each method based on the specific logarithmic expression you’re working with.

Have a look at this video if you need to review how to expand logarithms.

• Expanding Logarithms

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Expand Logarithms Worksheets.

 

More Expand Logarithms Worksheets

Printable
(Answers on the second page.)
Expand Logarithms Worksheet #1
Expand Logarithms Worksheet #2 (Include Radicals)

Online
Apply Law of Exponents (multiply)
Apply Law of Exponents (mixed)

Related Lessons & Worksheets

Logarithm Rules & Properties
Evaluate Logarithms by Expanding & Condensing

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