This activity explores the basics of evaluating logarithms.
In this lesson, we will be looking at a format that we use when we know an answer and a base. It is called a logarithm. For example,
can be rewritten as
and the answer is the x. Here are a couple examples of problems written in logarithmic form and their answers.
Using the above examples, what do you think the answer (the exponent in exponential form) will be for:
In the problem above,
6 is the base, and 36 is the arguement (answer of the exponential equation), so it can be rewritten as
Since six squared is thirty six, the answer is 2.
Using the above examples, what do you think the answer (the exponent in exponential form) will be for:
Using the above examples, what do you think the answer (the exponent in exponential form) will be for:
Using the above examples, what do you think the answer (the exponent in exponential form) will be for:
If you did not understand the smaller logs, take a look at these videos, and do not be afraid to email your teacher.
Sometimes, the argument ( big number after the log) is to big to see how many times the base ( little number after the log) goes into it. In these cases, use prime factorization to find the answer.
Since the base is 5, we will find how many times 3125 can be divided by 5.
Another way to think about this is to rewrite the base in an exponential equation:
Now we will use prime factorization to find the number of factors of five are needed to get 3125.
Look at the following work
Evaluate.
Evaluate.
Evaluate.
If there is no number written as the base of the log (the little number after the log), the base is 10.
For example in the following:
Evaluate.
Log 100
The base is 10 and it is the same as
What is the exponent we are looking for here?
Evaluate.
Do you understand this lesson thus far? What is a question you have? Try to be specific.
What do you think the answer to this is?
What do you think the answer to this is?
When the argument (big number beside the log) is 1 what happens?
What do you think the answer to this is?
What do you think the answer to this is?
When your base is a whole number and your arguement is a fraction, what happens in your result?
Name anything that might be confusing to you at this point.