**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 3:** Suppose that a base is 4 and exponents are 5, 2, and 3. We could
solve the exponential problem by
calculating ,

, and separately 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 , changing the base of 4 to either 10 or e and calculating the results.

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

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

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour