Big Ideas Math [IM3]: 5.2 - Logarithms and Logarithmic Functions (Lecture & Problem Set)

Logarithms are a brand new function for you, and with newness comes a bit of a learning curve. There will be confusion, frustration, and denial, but with all of that this section goes extremely slowly and holds your hand through the process. If not, I'm hoping my video does enough of this.

Logarithms ("logs" for short) are inverses of exponentials. You'll hear me say this routinely throughout the video. The book says it best: We know that 2^2 = 4 and 2^3 = 8, but if 2^x = 6 then what is x? 2 to what power gives you 6? Logarithms answer that. Ironically enough, you won't learn how to EVALUATE that in your calculator in this particular section because we want to exercise other properties first, but you will know how to write an exact answer. Applying the log function to a number (given a certain base) results in an answer, and that answer is an exponent. I can't type the notation here, but you'll see it plenty in the video, to where the answer to that question for x is "log base 2 of 6." The function for logarithms literally is "log."

Your calculator can easily compute the common logarithm (log, or "log base 10") and the natural log (ln, or "log base e"), and through examples I show how those work on the calculator so you can get used to how we're converting from logarithmic to exponential form, and vice versa. Changing base though, as I said, is a different thing entirely, and we'll learn that in another section.

We learn how to find inverses of logs as exponents so we can begin our understanding of what their graphs look like. I throw little hints on how we'll be graphing them in general moving forward to Section 5.3, so pay close attention to that block of problems if you choose to watch that portion of the video.

Logs are a fundamental part of this chapter, so laying the groundwork in this section is crucial for our understanding moving forward.

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*TIMESTAMPS (separated by section)*

(0:00:00) Introduction
(0:01:24) Lecture overview
(0:24:45) Problem #1-4
(0:26:59) Problem #5-10
(0:29:52) Problem #11-16
(0:33:09) Problem #17-24
(0:40:13) Problem #27-32
(0:46:10) Problem #33-34
(0:51:32) Problem #35-40
(0:55:07) Problem #41-42
(0:59:09) Problem #43-52
(1:07:28) Problem #53
(1:10:43) Problem #54
(1:14:51) Problem #55-60
(1:33:37) Problem #61-64
(1:44:49) Problem #65
(1:46:02) Problem #66
(1:49:40) Problem #67
(1:56:03) Problem #68
(2:00:20) Problem #69
(2:06:45) Problem #70
(2:08:56) Problem #71

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