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### Course: Algebra 2 > Unit 8

Lesson 3: The change of base formula for logarithms- Evaluating logarithms: change of base rule
- Logarithm change of base rule intro
- Evaluate logarithms: change of base rule
- Using the logarithm change of base rule
- Use the logarithm change of base rule
- Proof of the logarithm change of base rule
- Logarithm properties review

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# Logarithm properties review

Review the logarithm properties and how to apply them to solve problems.

## What are the logarithm properties?

Product rule | ||

Quotient rule | ||

Power rule | ||

Change of base rule |

*Want to learn more about logarithm properties? Check out this video.*

## Rewriting expressions with the properties

We can use the logarithm properties to rewrite logarithmic expressions in equivalent forms.

For example, we can use the product rule to rewrite $\mathrm{log}(2x)$ as $\mathrm{log}(2)+\mathrm{log}(x)$ . Because the resulting expression is longer, we call this an

**expansion**.In another example, we can use the change of base rule to rewrite $\frac{\mathrm{ln}(x)}{\mathrm{ln}(2)}$ as ${\mathrm{log}}_{2}(x)$ . Because the resulting expression is shorter, we call this a

**compression**.*Want to try more problems like this? Check out this exercise.*

## Evaluating logarithms with calculator

Calculators usually only calculate $\mathrm{log}$ (which is log base $10$ ) and $\mathrm{ln}$ (which is log base $e$ ).

Suppose, for example, we want to evaluate ${\mathrm{log}}_{2}(7)$ . We can use the change of base rule to rewrite that logarithm as $\frac{\mathrm{ln}(7)}{\mathrm{ln}(2)}$ and then evaluate in the calculator:

*Want to try more problems like this? Check out this exercise.*

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