The properties of logarithms assume the following about the variables M, N, b, and x.

- log bb = 1
- log b1 = 0
- log bb x= x
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b logbx= x
- log b( MN) = log b( M) + log b( N)
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Note: Don't confuse
with
.
- To find the latter, first evaluate each log separately and then do the division.
- log bM x= x log bM
- If log bx = log by , then x = y.
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This is known as the change of base formula.
Example 1
Simplify each of the following expressions.
- log 7 7
- log 5 1
- log 44 3
- 6 log65
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Example 2
If log 3 5 ≈ 1.5, log 3 3 = 1, and log 3 2 ≈ 0.6, approximate the following by using the properties of logarithms.
- log 3 10
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- log 3 25
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- log 3 1.5
- log 3 200
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Example 3
Rewrite each expression as the logarithm of a single quantity.
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