Name: Properties of logarithms
Uploaded: 2023-05-29T03:05:30.624Z
Duration: 7 min 35 s
Description: In this short video I introduce and discuss the properties of logarithms. There are really only three! Check out my other videos to see how to apply these properties to evaluate logarithms and solve logarithmic equations.

In this short video I introduce and discuss the properties of logarithms. There are really only three! Check out my other videos to see how to apply these properties to evaluate logarithms and solve logarithmic equations. 

Algebra 2

Hello there! My name is Colin, and I have nine years of experience tutoring math and science. I am a PhD candidate in the UC Berkeley-UC San Francisco joint bioengineering program. My strong background in STEM qualifies me to tutor math and science up through lower-division college courses. Aside from my academic qualifications, I believe that it is my genuine passion for math and science that makes me an effective tutor for students of all learning styles.  

As a tutor, my goal is not to impress students with how much I know. Rather, my goal is to show my students how easily math and science concepts can come to them when they are presented the material in a straightforward way. The late physicist, Richard Feynman, posited that the ability to explain complicated ideas in a simple manner is the true mark of understanding. I agree with this assertion, and I make it my goal each tutoring session to explain even the most complex phenomena in a simple way, so that my student will come away from the lesson with confidence that they grasped the information. Additionally, I emphasize a strong understanding of the fundamentals because both math and science are heavily inductive disciplines; many of the theorems and laws are founded on other, more fundamental principles. I have personally experienced the discouragement of trying to learn material that is beyond my level of preparedness, and so I can empathize with students who are in that boat. Fortunately, I have learned that the remedy is always a return to, and a strengthening of, the basics. That is the approach I take with students who find themselves struggling in a course. 

My online teaching platform is a “black board” drawing program that my students can follow along with as I explain concepts and solve problems. I simply share my screen with them during the session and at the end I take a screenshot of the notes and email it to my students for their reference. I hope this brief explanation of my qualifications and teaching style has provided a clear image of what you can expect from me as your tutor. I am eager to hear from you and help you succeed in your academic goals!

Properties of logarithms 

2bf2255c-05e8:37755;isclassifiedstrendingsuggestionsenableddt:42136;316f64c0-2415:46048;b2454379-d6cf:44572;335d7519-3303:46159;31885555-099a:47313;9979286f-d859:47315;i9de8100:55497;ei83g319:53872;47h3f766:58362;fg008402:58376;i6jj6667:86739;istutorredesignv2_1:73124;2b6i0532:68197;a5gbd220:61179;blogpwt:71359;5db3b892:67466;2a2j8400:70238;b534g232:70741;j91hb444:69773;18h21436:69961;85h98405:81245;0eie7335:76839;cia78296:75037;9b4gd804:78753;4d465237:81260;deisn977:110326;1d789912:110325;slcardst:87990;searchranking_newpqs:91321;b1ff5649:88417;d9c7i206:87231;ajgj0920:88926;dgigc739:92611;15gbg809:92228;6ij3b180:95553;90ahj157:94513;2a718373:100011;gg41j822:94817;3i5dg498:97157;437bb176:97771;06ieg414:100430;9ab7j510:99496;86afb588:101093;bfb37872:105751;7f8gg909:114000;eh7a9388:114646;

Arithmetic

Statistics

Algebra

Physics

Geometry

AP Chemistry

Elementary Math

Linear Algebra

Math

Biology

AP Biology

Pre Algebra

Pre Calculus

AP Calculus

Basic Math

Trigonometry

Python

Algebra 1

Calculus

Chemistry

AP Physics

Elementary

Middle School

High School

College

The purpose of Phi Theta Kappa shall be to recognize and encourage scholarship among two-year college students. To achieve this purpose, Phi Theta Kappa shall provide opportunity for the development of leadership and service, for an intellectual climate for exchange of ideas and ideals, for lively fellowship for scholars, and for stimulation of interest in continuing academic excellence.

Jack Kent Cooke Summer Internship Stipend

Jack Kent Cooke Undergraduate Transfer Scholarship

Stem Cell Engineering Pre-doctoral Fellowship

Jack Kent Cooke Graduate Scholarship

I was a tutor in the Math Lab at Miramar College. Here, I tutored pre-algebra through multi-variable calculus.

Math Tutor

I have been tutoring math and science subjects through online platforms since 2014, and have provided over a thousand hours of tutoring to students of all ages and educational levels.

Math and Science Tutor

At the PLACe I helped students in various English and humanities courses with their essay writing. Generally, students would ask me to read their drafts and I would advise them on grammar, syntax and structure.

Essay Writing Tutor

I was a GSI for BIOENG 131 Introduction to Computational Molecular and Cell Biology:

This class teaches basic bioinformatics and computational biology, with an emphasis on alignment, phylogeny, and ontologies. Supporting foundational topics are also reviewed with an emphasis on bioinformatics topics, including basic molecular biology, probability theory, and information theory.

I helped students with coding in Python for homework assignments, as well as answer general questions about course topics.

Graduate Student Instructor

I was a GSI for BIOENG 115 Tissue Engineering Lab:

This class provides a conceptual and practical understanding of cell and tissue bioengineering that is vital for careers in medicine, biotechnology, and bioengineering. Students are introduced to cell biology laboratory techniques, including immunofluorescence, quantitative image analysis, protein quantification, protein expression, gene expression, and cell culture.

English

Japanese

I view algebra like a game: there are simple rules that govern what you can do, and if you know and understand the rules, the game is a whole lot easier. If algebra seems to be a struggle for a student, I can help them identify the basic concepts (i.e. rules) on which they need to strengthen their understanding. Algebra is an essential tool I use to solve a myriad of problems every day as an engineer, and so I am intimately familiar with its many different topics, and perhaps because I understand its value, I genuinely enjoy teaching algebra to others.  

I remember what it was like to personally struggle with algebra, and I know the most common pitfalls which make it seem more difficult than it actually is. Because of this experience, I am quite adept on picking up on my students' weak  points, and helping them clear up fuzzy understandings of the rules of algebra. I started teaching algebra six years ago when I first started teaching it to myself. Since that time, algebra has been the subject I have tutored the most, and I believe I have become quite good at helping students master concepts that were once most challenging for them. 

My goal is to help my students not only raise their algebra grades to all As, but more importantly, to help them establish a rock-solid base in algebra on which to build higher math skills. I do this by:

1. Providing each algebra student with a thorough, in-depth review of the basic concepts in which they have not yet mastered

2. Demonstrating central problem-solving techniques that are essential for all levels of math (and science)

3. Providing them with practice problems to do in between our sessions so that they have the opportunity to solidify the information and skills they learn. 

There are amazing careers waiting for those who are educated in higher mathematics, and everyone should have the opportunity to pursue them. It all begins with a solid foundation in algebra.

The lesson was excellent and really helped a lot.  I did much better on the exam the next day than i would have.  

I have been working with Colin for the past two semesters as a sophomore in college. He has helped me with both my 1st and 2nd physics courses, both of which I have received an 'A' letter grade in. Colin is super helpful at answering any questions you might have and if you are struggling with understanding a concept he will try to find new and helpful descriptions until you are able to understand it! There were several times throughout this past year that I was struggling with a specific homework problem or concept and he would go over our lesson time or send me an in-depth video recording of him answering my question/explaining an example to help me succeed. I'm forever grateful!


Extremely happy with Colin as he helped our son for his test-out. He has a clear understanding of the subject matter and a very effective way of explaining it. We will continue using his expertise for duration of my son's schooling and when ever he needs help.

Five stars and 2 thumbs up!

Colin is an amazing teacher that helps you understand the most confusing equations, lessons, homework, and labs! He can easily connect with you with many resources that will help benefit you outside of lessons, and dives into problems with deep analysis to help you better understand it. 

Colin is a super knowledgeable tutor in math and physics.  He is helping my daughter with IB Math and IB Physics.  He is patient and he is very good at explaining both subjects to her in a way that’s easy for her to understand.  She is very comfortable working with him.  I appreciate his flexibility and willingness to help whenever she needed extra help.  Highly recommended.

I've been struggling with Calculus 3, but with the help of Colin, I am understanding the difficult concepts much quicker. He explains everything in such detail and in a way that's very easy to understand. I highly recommend Colin if you're having difficulty in a hard class.

I had the absolute pleasure of working with Colin for my linear algebra course, and I can confidently say that he is an outstanding tutor. From the moment we started our sessions, I was impressed by his deep understanding of the subject matter and his ability to explain complex concepts in a clear and approachable manner.

Colin's teaching style is truly one-of-a-kind. He possesses a rare talent for breaking down intricate mathematical concepts into digestible chunks, making even the most challenging topics seem manageable. His patience and willingness to adapt to my learning pace created a comfortable and productive learning environment.

Not only did Colin help me grasp the material, but he also instilled in me a newfound confidence in my mathematical abilities. Thanks to him, I not only aced my exams but also developed a deeper appreciation for the subject.

I wholeheartedly recommend Colin to anyone seeking a tutor who is not only knowledgeable but also genuinely cares about their students' success. He is a true gem in the world of tutoring, and I am grateful for the invaluable support he provided throughout my linear algebra journey. Thank you, Colin!

Colin is an amazing tutor. I have done both physics and SAT math prep lessons with him and he broke down many concepts and solving techniques so that it would be easier to understand. His method of teaching (posing questions, sending over digital notes, extra resources, etc) was really helpful for me, and you can tell he really knows what he's doing. I highly recommend anyone looking for a tutor to take lessons with Colin.

He knows what he is talking about. He is very professional and patient. He actually knows how to teach. He teaches multiple subjects which makes him even better. If you want someone to teach you math and science, he is your guy. I’ve been taking lessons from him since the summer and he will give you in depth lessons about the subjects that you are taking. He explains subjects very well and makes them very easy to understand.

Colin is an excellent instructor.  My two kids look forward to take his lessons each week. He is very patient and explains the lessons very clearly. I highly recommend him to others looking for a tutor.

Colin is simply amazing. He is the best tutor I’ve worked with. He really knows his stuff and is able to break hard topics down so they are easier to grasp. He really took the time to make sure I understood things and never made me feel incompetent. I 100% recommend him. Your grade will thank you for it!

I am a student of Colin's and I have been learning from him for at least 4-5 months. I have been struggling with math before because I wasn't taught by a tutoring center that couldn't explain in a clear manner to me. Colin is an extremely knowledgable teacher in math. He has great explanations that go in depth about the math being taught rather than the surface level of math. He has a lot of knowledge in this field as well as anything to do with biology. Overall, he is a genuine person and just a great guy in general!

Colin is a godsend. My daughter was struggling with chemistry and her confidence was suffering. Colin is knowledgeable, but also very kind and professional. He helped my daughter regain her confidence and increase her test/quiz scores. 10/10 highly recommend.

Colin is seriously awesome! He's got the patience of a saint, which is a lifesaver when you're wrestling with those tricky calculus problems. What really impressed me was how he used cool tech stuff to make learning way more fun and understandable. And talk about flexible – Colin always worked around my crazy schedule and customized his teaching to what I needed. So, if you're looking for a calculus tutor who's patient, tech-savvy, and super adaptable, Colin's your guy!

I've been working with Colin as my calculus tutor for the past six weeks, and I couldn't be happier with our sessions. Not only is he a fantastic tutor, but he also makes learning calculus genuinely enjoyable.

Colin's teaching style is engaging and relatable, which makes it easy to stay focused and interested during our sessions. He has a knack for breaking down complex concepts into understandable pieces, and I appreciate how he encourages questions and discussions. It's like having a conversation about calculus with a friend rather than a traditional tutoring session.

What's truly impressive is that Colin manages to keep the sessions fun while ensuring I'm making steady progress. His positivity and enthusiasm for the subject are contagious, making me genuinely excited to tackle calculus problems. Thanks to Colin, my six weeks of learning calculus have been not only productive but also enjoyable. I couldn't have asked for a better tutor.

In this video we see how to approach a polynomial division problem using the Polynomial Remainder Theorem, which cuts the time to solve down to just seconds from the minutes it would take using polynomial long-division or synthetic division. The key to acing the SAT is to recognize these types of shortcuts when they are possible!

SAT Math: When to use the Polynomial Remainder Theorem

In this short video we see how to recognize when the integral can be solved with a u-substitution, rather than using integration by parts.


Calculus II/Calculus BC - Integration by Parts: How to Recognize When it's Really a U-Sub

In this example we see how to use completing the square to solve the roots, or x-intercepts, of a quadratic.

Quadratic Equations - Completing the square: Solving for the roots

In this video we walk through a more complicated example of completing the square when the leading coefficient is not equal to one. 

Quadratic Equations - Completing the square: a more complicated example


In this video we walk through a simple example of completing the square. 


Quadratic Equations - Completing the square: a simple example

In this video I provide another walkthrough of the "wrap-around" method, this time with a more complicated integral. 

Calculus II/Calculus BC - Integration by Parts: Another Wrap-around Example

In this video we see how to solve a solids of revolution problem using the disk method.

How to solve: Solids of Revolution - Disk Method

In this video we work a machine learning math problem: find the principle components of a small dataset. This requires an understanding of covariance matrices, eigenvalues and eigenvectors from linear algebra.

Principle Component Analysis by Hand

In this video we cover how to apply integration by parts to a definite integral (i.e. when you have limits). We see that it is not too different from solving simple definite integrals.

Integration by Parts: Definite Integral Example

In this video we see the power of the tabular method by integrating a fairly difficult integral. The tabular method is quite handy for integrals that require several iterations of integration by parts, usually when you have a high degree polynomial paired with a trig or exponential function.

The Tabular Method for Integration by Parts

This video provides a gentle introduction integration by parts for indefinite integrals.

Colin S.

Properties of logarithms

Colin's Algebra 2 videos

SAT Math: When to use the Polynomial Remainder Theorem

Calculus II/Calculus BC - Integration by Parts: How to Recognize When it's Really a U-Sub

Quadratic Equations - Completing the square: Solving for the roots

Quadratic Equations - Completing the square: a more complicated example

Quadratic Equations - Completing the square: a simple example

Calculus II/Calculus BC - Integration by Parts: Another Wrap-around Example

How to solve: Solids of Revolution - Disk Method

Principle Component Analysis by Hand

Integration by Parts: Definite Integral Example

The Tabular Method for Integration by Parts

Introduction to Integration by Parts

Properties of logarithms

Teacher Reviews (113)

Book online lesson

Completing the Square

Related Subjects