# Condense Logarithms Worksheets

There are four sets of logarithm & exponential worksheets:

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

### How to condense logarithms?

There are two sets of condensing logarithm worksheets.

• Condense Logarithms.

Condensing logarithms means combining multiple logarithmic terms into a single, simplified logarithmic expression. Here are some techniques for condensing logarithms:

1. Product Rule for Logarithms:
The product rule for logarithms states that
logb(M) + logb(N) = logb(MN).
This rule allows you to combine two separate logarithmic terms that are being added into a single logarithmic term.
For example, to condense log2(5) + log2(x):
log2(5) + log2(x) = log2(5x)

2. Quotient Rule for Logarithms:
The quotient rule for logarithms states that
logb(M) - logb(N) = logb(M/N)
This rule allows you to combine two separate logarithmic terms that are being subtracted into a single logarithmic term.
For example, to condense log5(8) - log5(x)
log5(8) - log5(x) = log5(8/x)

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

These techniques can help you condense logarithmic expressions and simplify them into a more compact form. 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 condense logarithms.

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

### More Condense Logarithms Worksheets

Printable
Condense Logarithms Worksheet #1
Condense Logarithms Worksheet #2 (Include Radicals)

More Printable Worksheets

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