## Pre-Calculus Tutorial

*expanding logarithms using the property rules*

#### Intro

Before attacking this problem, you should be familiar with these three rules:

“b” represents the base

1: Product Rule:

–**log** b (XY) = **log** b X + **log **b Y

2: Quotient Rule:

–**log **b (x/y) = **log **b X – **log **b Y

3: Power Rule:

–**log **b M^p = p **log **b M

#### Sample Problem

**log **b (X^2 Y/Z^6)

#### Solution

**log **b (X^2 Y/Z^6)

The first step is to use the quotient rule to eliminate the fraction

1: **log **b (X^2 Y/Z^6) => **log ** b X^2 Y –**log ** b Z^6

The next step is to use the product rule

2:**log ** b X^2 Y –**log ** b Z^6 => **log **b x^2 + **log **b Y – **log **b Z^6

The third and last step is to use the power rule

3: **log **b x^2 + **log **b Y – **log **b Z^6 => 2 **log **b X + **log **b Y – 6 **log **b Z

# About The Author

Math, Pre-Calculus, English, Writing |

Having a background as a C-130 Crew Chief for the U.S. Air Force has compelled me to peruse a degree in Mechanical Engineering. The passion developed while in technical school and at my duty station has transferred to my studies, resulting in a strong mathematical foundation. Prior to enlistin... |

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