Logarithms... How? (NancyPi)

MIT grad introduces logs and shows how to evaluate them. To skip ahead: 1) For how to understand and evaluate BASIC LOGS, skip to time 0:52. 2) For how to evaluate weirder logs, including the log of 0, 1, a FRACTION, or a NEGATIVE number, skip to time 6:44. 3) For NATURAL LOGS (LN X), skip to time 11:17. 4) For even weirder logs, including SOLVING for X and using the CHANGE-OF-BASE formula, skip to time 14:56. Nancy formerly of MathBFF explains the steps.

1) BASIC LOGS: you can read log notation as "log, base 3, of 9 equals X". The small (subscript) number is called the base. You can always evaluate a log expression by rearranging it into something called exponential form. Every log expression is connected to an exponential expression. In this example, the log is connected to the exponential form "3 to the X power equals 9". This means, "3 raised to what power gives you 9?" Since 3 raised to the power of 2 equals 9, the answer for X is 2. This is also the answer for the value of the log expression. The log is always equal to the power (or exponent) in the exponential version, and in this case it equals 2. If you want, you can find the log value in your head just by asking yourself what power you need in order to turn the base number into the middle number ("argument" number). Note: if there is no base number in the log expression (no little subscript number), then the base is 10, since 10 is the default base.

2) WEIRDER LOGS (log of 0, 1, a negative number, or a fraction): you can use the same steps to rearrange log expressions that have a fraction, negative number, 0, or 1 in them. You can still rearrange them to be in exponential form just like you can with the basic logs from earlier. The log of 1 will always be 0, since 0 is the only power that can turn a base into 1. The log of 0 will always be undefined, since no power can turn a base into 0. The log of a negative number is undefined in the real number system, since no real power can turn a positive base into a negative number.

3) NATURAL LOGS (ln x): the natural log is just a special type of log where the base is e (the special math constant e, which is approximately 2.718 if you plug it into your calculator). You can use the same steps for rearranging the log expression into exponential form. Just remember that ln x means log, base e.

4) EVEN WEIRDER LOGS (solving for X, change-of-base formula): even if there is an X variable in the log part of an equation, you can still rearrange the equation into exponential form. This will let you solve for X. Sometimes you might need to use the change-of-base formula to evaluate a log expression. If there is no whole number power you know that works, it may actually be a decimal power that you can find by using the change-of-base formula. For example, you can re-write log, base 2, of 7 as (log 7)/(log 2) and use your calculator to find the decimal number if you need it.

[dipta]

If you watch carefully, you'll see that she is teaching us logarithm. ( With due respect to @NancyPi who is an amazing teacher. )

[ivanr]

Senior in computer science now. I remember nancys videos helping me out a lot through calc 1 and 2. YouTubers like her are truly heroes.

[serenalizinnqui]

I love how, even though she's an MIT grad, she reasons through these problems like a beginner without assuming any steps. Her voice is so soothing, too. Thanks, Nancy!

[ShardCollector]

I wasn't even looking to learn this, but YouTube desided that it would be a good idea 😅 And I'm greatful I came, because Nancy is a natural teacher, but I'm equally impressed by her backwards writing skills, than in math skills 😊👍

[superlad]

After completing my Engineering Degree I am here to learn Logarithms again.

[ZstripeW]

Everybody's commenting on the math or how pretty she is... I'm over here trying to figure out how the heck she learned to write backwards so well!

[normaestien]

She makes log understandable. The snail concept is absolutely ingenious. And her notes at the top indicates exactly where to find what is needed instead of watching the whole video. Outstanding!

[nazlone]

I m 80.... I learnt logs in school.Then I realized I have forgotten a lot....but this video got me back.Thanks a lot .

[sarahlester]

You have broken this down in a way that's easy to understand! I also love that I can physically see you break down concepts your videos. A lot of other YouTuber's just record their screen's; you never actually see the person explaining steps. I think seeing the body language of someone teaching is crucial to effective learning. Thank you for the video!

[ece]

everyone talks about her beauty
and me thinking about her voice is so relaxing ^^

[umairxd]

I didn't learn half of the maths content due to lockdown. This is saving my life lol

[apaarshrivastava]

I'm Bachelor's of Arts student. But thought of learning something new today. Thank you for this session, its amazing to see your ways of explaining.

[ameerhamza]

Many people are asking how she is writing. She is writing on "glass board aka learning glass" on back side. Then computer flipping the image. She is surely writing using right hand

[fammy]

I love how she uses terms like "weird ", " Even weirder " ❤.. It definitely makes the classification easy .

[ayush-ax]

Fact : You did not come here for the logarithms.

[Erowens]

I really love how you start with easy stuff then gradually increase the difficulty. That seems like something a lot of math teachers, and especially professors struggle to do. Much easier to learn how something works with easy problems, then apply that understanding to harder problems. Than it is to learn how something works with harder problems.

[SteveInSunnyCA]

The way she appears to “write backwards” is simply that the video image has been flipped horizontally with software, or more likely by photographing her in a mirror. She is right handed and writing forward on the back side of glass. For any who still doubt that the image has been flipped, notice that her hair is parted on her right side in her lessons, but on her left side in her Q&A video.

[sonipwn]

I love and respect this girl so much! She has helped me and many others like me through some very rough time and I want nothing but the best for her! I hope she’s doing well

[TheMichman]

I wish that I would have had such a calm math teacher back in the day.

[officialstylechild]

You are the best math teacher I have seen. Everyone else’s explanation is more complicated than the math itself. Thank you for the easy explanation