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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 condense logarithms.
There are two sets of condensing logarithm worksheets.
Condensing logarithms means combining multiple logarithmic terms into a single, simplified logarithmic expression. Here are some techniques for condensing logarithms:
Product Rule for Logarithms:
The product rule for logarithms states that
log_{b}(M) + log_{b}(N) = log_{b}(MN).
This rule allows you to combine two separate logarithmic terms that are being added into a single logarithmic term.
For example, to condense log_{2}(5) + log_{2}(x):
log_{2}(5) + log_{2}(x) = log_{2}(5x)
Quotient Rule for Logarithms:
The quotient rule for logarithms states that
log_{b}(M) - log_{b}(N) = log_{b}(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 log_{5}(8) - log_{5}(x)
log_{5}(8) - log_{5}(x) = log_{5}(8/x)
Power Rule for Logarithms:
The power rule for logarithms states that
n log_{b}(M) = log_{b}(M^{n})
This rule allows you to move the coefficient as an exponent inside the logarithm.
For example, to condense 2 log_{3}(5)
2 log_{3}(5) = log_{3}(5^{2})
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.
Printable
(Answers on the second page.)
Condense Logarithms Worksheet #1
Condense Logarithms Worksheet #2 (Include Radicals)
Online
Apply Law of Exponents (multiply)
Apply Law of Exponents (mixed)
Evaluate Logarithms by Expanding & Condensing
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