Tutoring on Using the Definition of a Logarithm

Learning Objectives:

Understand Logarithm and Evaluate Logarithmic Expressions.Understand to write Exponential and Logarithmic Equations.

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.

logₐ x = y means ay  =  x.

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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