Expand Logarithms Worksheets

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There are four sets of logarithm & exponential worksheets:

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
    logb(MN)=logb(M) + logb(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
    logb(M/N) = logb(M) - logb(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
    logb(Mn) = n logb(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.

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

Expand Logarithms Worksheet

More Expand Logarithms Worksheets

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

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

Logarithm Rules & Properties
Evaluate Logarithms by Expanding & Condensing

More Printable Worksheets

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