Learning Objectives:

__Math Tutoring on Using the Definition of a Logarithm__

**A Logarithm** is just an **exponent.** Let us take a look at a more formal definition.

So since a **logarithm** is an exponent, it should seem logical that we can write a **log equation** as an **exponential equation.** Notice **"a" **would be the **base, y** would be the **exponent,** and **x** would be the number. We can say that **y** is the **power,** which we raise **"a"** to get **x **and we should note that **"a"** has to be greater than **0** and **"a" ≠ 1. “a”** is called the **logarithmic base.** Now let us go ahead and talk about common **log** and **natural log** because these are the two **logs** that we will find on your calculator. The **logarithm **with **base 10 **is called the **common log.** **Natural logarithms** are different than **common** **logarithms. **While the base of a **common logarithm **is** 10,** the base of a **natural logarithm** is the special number **e.** Although this looks like a variable, it represents a **fixed irrational number** approximately equal to** 2.718281828459. **

Thus **log₁₀ x = log x **and** logₑ x = ln x **where** x ˃ 0.**

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**Hook Questions:**

*1. **What does Ln stand for in math?*

*2. **What is the change of base formula?*

*3. **What is the difference between natural log and log?*

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