## Solve for the Unknown (Using Logarithms) Problems

#### Aligned To Common Core Standard:

**High School Functions** - HSF-LE.A.4

How to Solve for the Unknown (Using Logarithms)?
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.
Example: 2^{(x+2)} = 3^{X}
Step 1: Apply Log with base 10 (lnx) on both sides of the equation: ln 2^{x+2} = ln 3^{x}
Step 2: Apply Logarithmic rules to the new equation: (x+2) ln 2 = x ln 3 | x ln 2 + 2 ln 2 = x ln 3
Step 3: Place the like-terms together: x ln 2 - x ln3 = -2 ln 2
Step 4: Take the unknown value common: x(ln2 -ln3)= -2 ln2
Now, apply logarithmic rules here;
xln (2/3) = -2 ln2
x = -2 ln2 / ln 2/3
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.

### Printable Worksheets And Lessons

- 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.
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the rules; it's been a while.