# Exponents and logarithms relationship problems

### Relationship between exponentials & logarithms (practice) | Khan Academy

Exponents and Logarithms work well together because they "undo" each other ( so loga(m/n) = logam − logan, the log of division is the difference of the logs. Exponential and logarithmic functions can be seen in mathematical concepts in finance, specifically in compound interest. This relationship is. Introduction to Exponential and Logarithmic Functions. Logarithmic functions Explain the relationship between logarithmic functions and exponential functions .

- Relationship between exponentials & logarithms: tables

When this happens we will need to use one or more of the following properties to combine all the logarithms into a single logarithm. Once this has been done we can proceed as we did in the previous example. Show Solution First get the two logarithms combined into a single logarithm.

Show Solution As with the last example, first combine the logarithms into a single logarithm. It is also important to make sure that you do the checks in the original equation. Also, be careful in solving equations containing logarithms to not get locked into the idea that you will get two potential solutions and only one of these will work.

It is possible to have problems where both are solutions and where neither are solutions.

## Working with Exponents and Logarithms

There is one more problem that we should work. This is just a quadratic equation and everyone in this class should be able to solve that. Also, we can only deal with exponents if the term as a whole is raised to the exponent. It needs to be the whole term squared, as in the first logarithm.

### Working with Exponents and Logarithms

Here is the final answer for this problem. This next set of examples is probably more important than the previous set. We will be doing this kind of logarithm work in a couple of sections.

Example 5 Write each of the following as a single logarithm with a coefficient of 1. We will have expressions that look like the right side of the property and use the property to write it so it looks like the left side of the property. This will use Property 7 in reverse. In this direction, Property 7 says that we can move the coefficient of a logarithm up to become a power on the term inside the logarithm.

I'm raising something to the first power and I'm getting 2? What is this thing? That means that b must be 2. So b is equal to 2. You could say b to the first is equal to 2 to the first.

That's also equal to 2. So b must be equal to 2. We've been able to figure that out. This is a 2 right over here. It actually makes sense. Now let's see what else we can do. Let's see if we can figure out c.

## Exponentials & logarithms

Let's look at this column. Let's see what this column is telling us. That column we could read as log base b. Now our y is 2c. Log base b of 2c is equal to 1. Or we could read this as b, if we write in exponential form, b to the 1.

Now what's b to the 1. They tell us right over here that b to the 1. We get 2c is equal to 3, or divide both sides by 2, we would get c is equal to 1.

This is working out pretty well.