# Precalculus : Properties of Logarithms

## Example Questions

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### Example Question #61 : Properties Of Logarithms

Expand this logarithm:

Explanation:

Use the Quotient property of Logarithms to express on a single line:

Use the Product property of Logarithms to expand the two terms further:

Finally use the Power property of Logarithms to remove all exponents:

The expression is now fully expanded.

### Example Question #62 : Properties Of Logarithms

Expand the following logarithm:

Explanation:

Expand the following logarithm:

To expand this log, we need to keep in mind 3 rules:

1) When dividing within a , we need to subtract

2) When multiplying within a , we need to add

3) When raising to a power within a , we need to multiply by that number

These will make more sense once we start applying them.

First, let's use rule number 1

Next, rule 2 sounds good.

Finally, use rule 3 to finish up!

### Example Question #63 : Properties Of Logarithms

Completely expand this logarithm:

Explanation:

Quotient property:

Product property:

Power property:

### Example Question #64 : Properties Of Logarithms

Fully expand:

Explanation:

In order to expand the expression, use the log rules of multiplication and division.  Anytime a variable is multiplied, the log is added.  If the variable is being divided, subtract instead.

When there is a power to a variable when it is inside the log, it can be pulled down in front of the log as a coefficient.

### Example Question #65 : Properties Of Logarithms

Expand the following:

Explanation:

To solve, simply remember that when you add logs, you multiply their insides.

Thus,

### Example Question #66 : Properties Of Logarithms

Express the following in expanded form.

Explanation:

To solve, simply remember that when adding logs, you multiply their insides and when subtract logs, you divide your insides. You must use this in reverse to solve. Thus,

### Example Question #67 : Properties Of Logarithms

Completely expand this logarithm:

Explanation:

We expand logarithms using the same rules that we use to condense them.

Here we will use the quotient property

and the power property

Use the quotient property:

Now use the power property:

### Example Question #68 : Properties Of Logarithms

Expand the logarithm

Explanation:

In order to expand the logarithmic expression, we use the following properties

As such

### Example Question #69 : Properties Of Logarithms

Given the equation , what is the value of ? Use the inverse property to aid in solving.