Product Rule for Logarithms

Intro

Let’s show that

PROOF:
1. Let …. We can name it anything we like
2. Let …. Again we can name it anything we like

3. and … Equivalent exponential forms of the statements in steps 1 and 2.

4. .. Reason: If A=B & C=D, then AC=BD.

5. ..Reason: Property of exponents: AQ•AS=AQ+S.

6. .Reason: Taking log (base a) of both sides.

7. Reason: same expression as step 6

8. . Substituting from steps 1 and 2 into step 7

Sample Problem

Solution

EXAMPLE:
…. 2*2*2 = 8
… 2*2*2 *2=16

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