**Let a be a positive number such that a does not equal 1, let
n be a real number, and let u and v be positive real numbers.**

**Logarithmic Rule 1:**

**Example 1:** Suppose that a base is 6 and exponents are 3 and 5. We could solve the exponential problem by calculating and
and multiplying the results. and and their product is . You
could also solve the problem by first combing the exponents
.

The same is true of logarithms. Suppose you wanted to calculate
. You could
calculate the answer by first multiplying 216 by 7776, changing the base of
6 to either 10 or e and calculating the results.

Or you could first combine the logarithms using Rule 1 and then change the bases.

rounded to 8.

**Example 2:** Calculate .

**Solution:** Since a base is not indicated, we know that the base is 10. We can calculate the logarithms directly by first multiplying the 30 and the 5. Note that can be
written . By Rule 1 we can also write as

To write this problem in turns of exponents, note that the base is 10 and the exponents are 1.4771213 and 0.69897. , rounded to 30. , rounded to 5. We could also combine the bases

**If you would like to review another example, click on
Example. **

**Work the following problems. If you would like to review the answers and solutions, click on answer.**

**Problem 1:** Calculate .

**Problem 2:** Calculate .

**Problem 3:** Calculate .

**Problem 4:** Calculate .

**Problem 5:** Simplify and
write the answer in terms of a base 10. What assumptions must be made about
a, b, d, and d before you can work this problem?

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