Example 1: Expand the log expression .
Looking inside the parenthesis, we see a product of number and variables. The Product Rule doesn't say that there should only be two factors inside, in fact, there could be more. Okay, so we'll separate the main log expression as sum of four logs.
Example 2: Expand the log expression .
The inside of the parenthesis is a fraction that means I will first apply the Quotient Rule. Since the numerator is a product of 7 and x, I use Product Rule to break it up.
Example 3: Expand the log expression .
Okay, so this one is also in fraction so Quotient Rule is the first step. But now there's something "new" in this problem.
That is, the numerator contains a variable with exponent. This should be easy since Rule 3 or Power Rule can easily handle it. Just bring the exponent down to the left, that's it!
In addition, there's a radical expression in the denominator. Remember that a radical can be expressed as fractional exponent. Since this radical is square root that means the power is just ½.