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Properties
1. The domain of the logarithm function is (0, ∞ ) . In other terms, we can just plug positive numbers into a logarithm! We can't plug in zero or a negative number.
2. logb b = 1
3. logb 1 = 0
4. logb bx= x
5. blogb x = x
The final two properties will be especially useful into the next section. Notice that these last two properties tell us that,
f( x ) = b x and g( x ) = logb x
are inverses of each of other.
Following are some more properties which are useful in the manipulation of logarithms.
More Properties
6. logbxy= logb x + logb y
7. logb (x/y)= logb x - logb y
8. logb( xr) = r logb x
Note as well that there is no equivalent property to the first two for sums & differences. In other terms,
logb( x + y ) ≠ logb x + logb y
logb(x - y ) ≠ logb x - logb y
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