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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. log_{b} b = 1
3. log_{b} 1 = 0
4. log_{b} b^{x}= x
5. b^{log}_{b}^{ 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 ) = log_{b} x
are inverses of each of other.
Following are some more properties which are useful in the manipulation of logarithms.
More Properties
6. log_{b}xy= log_{b} x + log_{b} y
7. log_{b} (x/y)= log_{b} x - log_{b} y
8. log_{b}( x^{r}) = r log_{b} x
Note as well that there is no equivalent property to the first two for sums & differences. In other terms,
log_{b}( x + y ) ≠ logb x + logb y
logb(x - y ) ≠ logb x - logb y
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