Solving Logarithmic Equations... How? (NancyPi)

MIT grad shows how to solve log equations, using LOG PROPERTIES to simplify and solve. To skip ahead: 1) For solving BASIC LOG EQUATIONS, skip to 0:22. 2) For ONE LOG ON EACH SIDE (EQUALITY property), skip to 2:36. 3) For TWO LOGS ADDED together and equaling a number (PRODUCT property), skip to 5:25. 4) For MANY LOGS, SUBTRACTED and ADDED, and using the QUOTIENT property, POWER property, and the other properties of logarithms (log rules), skip to 9:53. This video focuses on solving logarithms in equations and explains how to check the solution for an extraneous solution. Nancy formerly of MathBFF explains the steps.

Solving logarithmic equations with LOGS ON BOTH SIDES: If you have one log on each side of the equation, with the same base, you can use the EQUALITY PROPERTY log formula.

If you have more than one log on a side of the equation (with the same base), you can use the PRODUCT PROPERTY (if the logs are added) or the QUOTIENT PROPERTY (if the logs are subtracted) to combine the logs into one log. If you have a number multiplied in front of a log, as a coefficient, you can use the POWER PROPERTY logarithm formula to bring the coefficient up as a power inside the log argument. Once you simplify the log equation using the product, quotient, and/or power properties, you can either 1) solve by using the equality property if you just have one log on each side (with same base), or 2) solve by rewriting into exponential form if you have a log on one side and a number on the other side. IMPORTANT - CHECK SOLUTIONS: When solving logarithmic functions, you have to CHECK your solutions for log equations. Any numbers you get as solutions you have to plug back into the original equation to check. If a solution does not work or gives an undefined value (for example: log of a negative number), then it is an "extraneous solution" and must be thrown out!

[t_zarc]

She out here saving grades in the middle of this corona pandemic

[markzart]

So far through lockdown, Nancy Pi, is beyonf doubt the most articulate mathematician on YouTube, taking the viewer through the process in baby steps so that you cab REALLY grasp what is going on. I wish my maths teachers had been a tenth as good as she is.

[laurathomas]

My students and I love your clear, neatly written, very well planned lessons.

[paulmaggiar]

Nancy, your videos are a pleasure to watch. I love the way you use a glass board, write clearly on it, and fast forward the writing. Your explanations are on point and you are also such an affable person. Thank you for all your help.

[andrienefrancis]

funny how i'm in math class and couldn't seem to grasp this until seeing your video. just in time before my mid semester test :)

[joshreilley]

I struggled for hours on this subject, but the way you break everything down is super helpful, I am finally starting to understand Logarithmic Equations.

[chloeyen]

Oh my god, she was writing normally! She used a mirror mode to make the video comprehensible.

[augustineyarngo]

Hello Nancy,
This Terrence Yarngo, who watched your youTube video for personal studies of calculus daily. You are a great teacher and I admired your methods of teaching calculus, and logarithms using both the chain and product rules. The process you use to solve problems, makes calculus much more easier to understand. Please keep up the wonderful work you're doing for student like me.

Thank you so very much for such an outstanding job!

Best regards,

Terrence Yarngo

[neoblackcyptron]

An excellent teacher. Teaching is a gift, not everyone has that gift. This lady has the gift to convey ideas in a simple manner.

[joshuabowman]

You pause on certain things just long enough that I think you are going to stumble over words, but then you pull it off flawlessly. It's like i'm trying to finish your sentence for you in my mind, but then it all gets smoothed over into a great explanation. Love the videos! Thank you very much!

[honeybee]

You don't have to wait for the tutor to write on the board. It is automatically fast forwarded for you . It will certainly saves you time. She is a very effective teacher. Thumbs up for her.

[rafoldstarking]

NancyPi. Your explanation is so efficient and elegant. I’ve got to follow you! On a side note, it was easier for me to follow your reasoning having reviewed the properties of exponents. But I wonder if it is going to make as much sense for first timers.

[ccsvenezuela]

I never closed Khan Academy so fast :-)

[DanniWearsPrada]

You gotta know you have LITERALLY SAVED MY LIFE through these videos. bless your heckin soul !!!

[senzekilesibiya]

Daaaamn these thing is sooo easy ..how come im only seeing your videos now...u saved my life ..i hated logs cause i didnt understand them..thank u sooo much

[tessagunderson]

this is the first time logs have actually made sense to me, also its nice to see a girl teaching these videos for once :)

[Catanddoglover-mfcz]

I love how you waste no time with the writing but still explain it in a way someone can understand it. I normally don't have the patience for all of the writing and tend to skip and end up missing important notes for the lessons. Thank you for you well planned lessons.

[whosMandoo]

You’re literally a godsend Nancy!!! Thank you so much 🤞🏽💕 time to pass this math 41 final

[mohammeddawd]

Nanacy you are the best. Because you approach is simple and bright to understand.

[joshuatovar]

Thank you so very much Nancy! You brought back my love for Math.