Logarithms are a type of mathematical equations that are used to compare exponential values. While they can be intimidating to learn and master, they can be a useful tool for solving complex mathematical problems. Story problems involving logarithms are no different. In this guide, you will learn the basics of logarithms, how to solve story problems involving logarithms, and some example story problems to practice your skills.

## What Are Logarithms?

Logarithms are mathematical equations that are used to compare exponential values. In their basic form, they use a base, which is a number that is raised to a power, which is represented by an exponent. The logarithm of a number is the power that the base needs to be raised to in order to equal that number. For example, the logarithm of 100 with a base of 10 would be 2, because 10 to the power of 2 is 100.

## How To Solve Logarithm Story Problems

When solving logarithm story problems, the first step is to identify the base and the exponent. The base is usually identified as a variable, such as x. The exponent is usually identified as an equation or a numerical value. Once the base and the exponent have been identified, the equation can be solved using the logarithm formula. The formula for solving logarithms is log_{b}(x) = y, where b is the base, x is the exponent, and y is the answer.

## Example Story Problems

### Example 1

A logarithmic equation has a base of 4 and an exponent of 9. What is the logarithm of 4 to the power of 9?

To solve this problem, use the logarithm formula. The formula is log_{b}(x) = y, so in this case, the equation would be log_{4}(9) = y. To solve the equation, plug in the values for the base and the exponent, and solve for y. The answer is y = 2, so the logarithm of 4 to the power of 9 is 2.

### Example 2

A logarithmic equation has a base of 5 and an exponent of 7. What is the logarithm of 5 to the power of 7?

To solve this problem, use the logarithm formula. The formula is log_{b}(x) = y, so in this case, the equation would be log_{5}(7) = y. To solve the equation, plug in the values for the base and the exponent, and solve for y. The answer is y = 1.4, so the logarithm of 5 to the power of 7 is 1.4.

## Conclusion

Logarithms can be a difficult concept to understand and master, but with practice and understanding of the basics, they can be a useful tool for solving complex mathematical problems. In this guide, you have learned the basics of logarithms, how to solve story problems involving logarithms, and some example story problems to practice your skills. With a little practice, you will be able to solve any logarithm story problem with ease.