# Logarithmic Equations Worksheets

In this section of our site, we learn how to manipulate logarithmic equations to solve for missing variables. This can make students have to go the extra mile to find that skill that they lacked during basic operations. We encourage you to help your students get into the habit of understanding the pulse of the equation before they go in and try to solve for unknown values. Often you will find that there is a simple approach to solving most if not all of these problems. These worksheets and lessons will help students learn to solve for unknowns within logarithmic equations.

### Aligned Standard: HSF-LE.A.4

- Solve For x Step-by-Step Lesson- We work on isolating the variable in this equations. Logs sure make it a bit more difficult.
- Guided Lesson - Three more to test your will on logs and their use in equations.
- Guided Lesson Explanation - I give you a quick refresher on some properties that you need to remember.
- Practice Worksheet - This picture is what some students thought would be funny to doodle on their paper when doing this in class.
- Matching Worksheet - This is a very interesting set of problems for you to work with.
- Calculate the Value Five Pack of Worksheets - Bring all of these math sentences, if you will, to a conclusion.

- Answer Keys - These are for all the unlocked materials above.
- Homework Sheet - You will find ten problems that cover the gamut of the types of sum and difference problems that you will encounter with these equations.
- Quiz - You will see how you stand with this skill everything is set out with the two operations we have been working with to solve for the unknown.

### How to Solve Logarithmic Equations?

Solving logarithmic equations is a challenge for many students. Before you start solving a logarithmic function, you need to understand its types. Once you have a good handle on the anatomy, you will start to begin to understand how to adjust your approach as you become more familiar with these equations. There are two underlying principles that we need to take into account when we are looking at these equations. The value of the unknown variable can be positive, negative, or even worth zero. You just cannot have a logarithm of zero or a negative number.

There are generally two types of logarithmic equations.

The first type looks like log_{b}M = log_{b}N -> M = N.

The second type looks like log_{b} M = N -> M = b^{N}

To solve logarithmic equations, you have to follow some rules;

Product Rule: log_{b}(m × n)= log_{b}m + log_{b} n

Quotient Rule: log_{b} (m / n)= log_{b} m - log_{b} ^{n}

You can use this information to solve logarithmic functions.

Example: Solve 3=log_{2}x + log_{2}5

When you see the equation, you can immediately spot the product rule being applied on it. So, you use the product rule to simplify the equation.

3 = log_{2}(x+5)

We can now apply the type 2 logarithmic function here and the equation becomes;

2^{3} = x+5 | 8 = x + 5 | x = 3

This is how you can use the type 1, type 2, and both rules to solve a logarithmic function.

If you do not quickly see any type of these rules that may apply, see if you can reduce or condense the expressions on either set of the equal symbol. You can do this by combining any like terms or removing multiples. Remember, what ever you do to one side of the equation you must also do to the other.

This type of math is found most prevalent in science labs that work with very large or small scales. You will also come across this in many modern applications of computer software.