## Express as a Single Logarithm

#### Aligned To Common Core Standard:

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

How to Express Mixed Log Values as a Single Logarithm -
A logarithm (or simply 'log') is a mathematical tool that is used to solve complex exponential equations using a relatively simpler technique. It can be applied in long expressions like x^{3} - y^{2} + z^{5}. There is a certain method of expressing exponential expressions in terms of logs. First, the exponent is written, then log and then the variable part. For example, in this case, the equation will become 3log(x) - 2log(y) + 5log(z) after it is written with log. But how to express these long expressions as a single logarithm?
There are a few logarithmic identities. When two log terms are being subtracted, we can divide them by each other and write them with log as a single log term. Similarly, if two log terms are being added to each other, we can multiply them with each other and write them with log as a single log term. In the case discussed above, after the implementation of log identities, the expression will look like this:
x^{3} - y^{2} + z^{5} = 3log(x) - 2log(y) + 5log(z) = log(x^{3}) - log(y^{2}) + log(z^{5}) = log(x^{}3/y^{2}) + log(z^{5}) = log((x^{3}/y^{2}) . z^{5})
Here is how mixed log values are expressed as a single logarithm. These worksheets and lessons help students understand how to convert logarithm that are undergoing operations into a single value.

### Printable Worksheets And Lessons

- Sums and Difference of Logs Step-by-Step Lesson- See if your students can come up with a good explanation for the image.
- Guided Lesson
- Just a bunch more logs to throw on the fire. By fire, I mean your brain.

- Guided Lesson Explanation - The process is very similar regardless of the operation that is included in the mix.
- Practice Worksheet
- Combining the operations found in an algorithm is just so interesting.

- Matching Worksheet
- Match the values to the log operations that have created them.

- Express as a Single Logarithm Five Pack of Worksheets - It is kind of like saying, "Combine Like Terms!" Almost!