# Solve for Unknowns In Logarithms Worksheets

We explore a wide variety of techniques that you can use to manipulate equations that contain logarithms with them. You need to remind yourself that the counter to a logarithm is an exponent and vice versa. That simple fact with help you begin to learn how to isolate unknown variables within equations. This is how you can solve an exponential function with an unknown value using logarithmic functions. Students learn how to solve portions of logarithms using basic algebraic approaches.

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

- Solve for B Step-by-Step Lesson- This problem spins right of the exponential to logarithm conversion problems.
- Guided Lesson - The image definitely is a depiction of what I did when I first saw these problems again. It's been a long time, since we last met.
- Guided Lesson Explanation - The nice thing with these problems is that they are very easy fro people that have solid algebra skills.
- Practice Worksheet - I can't seem to make up my mind as to whether x or b are my favorite variable. I promise to use more variables in the future.
- Matching Worksheet - Find the value of the variable in each equation.
- Solve for the Unknown Five Pack of Worksheets - Can you find the variable. I had to review this a little before creating this section. I forgot the rules; it's been a while.

- Answer Keys - These are for all the unlocked materials above.
- Homework Sheet 1 - You will need to evaluate all of these equations and solve for the missing variable.
- Homework Sheet 2 - You will find that the solutions are often in fractional form.
- Practice Worksheet 1 - We included a greater number of brackets on this worksheet to give you more practice with them.
- Practice Worksheet 2 - Countering the operations is a good habit to get into.
- Quiz 1 - This is a nice assessment that will give you a baseline of where you stand with these skills.
- Quiz 2 - Tthe first problem is the most challenging and then it is all downhill from there.

### Solving for Unknowns in Logarithmic Equations

An equation that contains a logarithm is considered a logarithmic equation. There are various applications of logarithmic functions. One of the most common applications is that it can be used to solve exponential functions for unknown values. The situation where you cannot write exponents with a common base to solve for unknown, you need to use logarithms.

There are a number of things that you should consider when you are solving logarithmic equations. It all starts by making sure that if you have log on either side of the equation that you contract them. Once you have contracted them you will need to exponentiate it to get rid of logs. This will produce a basic algebraic equation which you are accustomed to by now.

An exponent is a shorthand method we use to express the number of times a number is multiplied by itself. A logarithm is its counterpart. It goes in reverse. When we are solving logarithmic equation, we can use them to counterbalance one another.

Example: log_{3} (4x + 5) = 4

**Step 1:** We can evaluate this by making it into a single log in the equation where the coefficient is one and the constant can be found on the other side of the equal sign. The exponential form of the would be: 4x + 5 = 3^{4}

**Step 2:** Solve for x. We first evaluate the exponent to be: 4x + 5 = 81

4x = 76

x = 19