Properties of exponential form, Mathematics

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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^xand 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_bxy= 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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