# Rewrite as a sum or difference of multiple logarithms help Example 5 Write each of the following as a single logarithm with a coefficient of 1. Example 2: Combine or condense the following log expressions into a single logarithm: The difference between logarithmic expressions implies the Quotient Rule. When we say simplify we really mean to say that we want to use as many of the logarithm properties as we can.

This is how it looks when you solve it.

### Logarithm calculator

In this problem, watch out for the opportunity where you will multiply and divide exponential expressions. Unnecessary errors can be prevented by being careful and methodical in every step. Next, utilize the Product Rule to deal with the plus symbol followed by the Quotient Rule to address the subtraction part. Properties 3 and 4 leads to a nice relationship between the logarithm and exponential function. Here is that step for this part. Just a reminder, you add the exponents during multiplication and subtract during division. Also, note that there are no rules on how to break up the logarithm of the sum or difference of two terms. This is how it looks when you solve it. This next set of examples is probably more important than the previous set. Rule 3: Power Rule The logarithm of an exponential number is the exponent times the logarithm of the base. Other textbooks refer to this as simplifying logarithms. It needs to be the whole term squared, as in the first logarithm. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number. Practice with Worksheets.

Other textbooks refer to this as simplifying logarithms. The second logarithm is as simplified as we can make it. Here is that step for this part. Remember that Power Rule brings down the exponent, so the opposite direction is to put it up. Therefore, we need to have a set of parenthesis there to make sure that this is taken care of correctly. The reason for this will be apparent in the next step. This means that we can use Property 5 in reverse.

## Log base properties

Other textbooks refer to this as simplifying logarithms. In these cases it is almost always best to deal with the quotient before dealing with the product. This is an interesting problem because of the constant 3. Here is the answer for this part. This is a nice fact to remember on occasion. Rule 2: Quotient Rule The logarithm of the quotient of numbers is the difference of the logarithm of individual numbers. We have to rewrite 3 in logarithmic form such that it has a base of 4. This is how it looks when you solve it. But, they all mean the same. Example 2: Combine or condense the following log expressions into a single logarithm: The difference between logarithmic expressions implies the Quotient Rule. We will be doing this kind of logarithm work in a couple of sections. Remember that Power Rule brings down the exponent, so the opposite direction is to put it up. Rule 5: Identity Rule The logarithm of a number that is equal to its base is just 1.

The square root can definitely simplify the perfect square 81 and the y12 because it has an even power. It needs to be the whole term squared, as in the first logarithm.

### Quotient property of logarithms

This is a nice fact to remember on occasion. Example 3: Combine or condense the following log expressions into a single logarithm: Start by applying Rule 2 Power Rule in reverse to take care of the constants or numbers on the left of the logs. In these cases it is almost always best to deal with the quotient before dealing with the product. The square root can definitely simplify the perfect square 81 and the y12 because it has an even power. Example 4 Simplify each of the following logarithms. Next, utilize the Product Rule to deal with the plus symbol followed by the Quotient Rule to address the subtraction part. Therefore, we need to have a set of parenthesis there to make sure that this is taken care of correctly.
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