I’m learning more advanced math that my school would not offer to me right now. I just want to say that your videos are incredibly helpful in my advanced math journey.
It's interesting, and it's funny that in school we used logs to find the answer to a complicated multiplication by adding them and not the other way round as in this video. We also used slide rules that worked because of their logarithmic scale.
Doubt from 1st lecture -- 1. What is log e , give examples 2. I didn't understood 5^log5¹² =12 in 4:28 I Am class 8 th student of india but still almost the whole 1st lecture Thank you so much sir You are best teacher I have ever seen
First question: log base e, or natural log or ln(x) is a special case of a logarithm base. The e stands for Euler's number, which is about 2.71828. Euler's number is a transcendental number like pi, where it is has a never ending or repeating decimal expansion, and where it cannot be calculated with a finite combination of arithmetic, powers, and roots. It is usually a series or a limit that you can use to calculate it. ln(x) = y, is how you solve the equation A = e^x for x, where A is a number you know, e is a standard constant, and x is a number you don't know. The reason we are interested in this, is that e^x has special properties in calculus, where its derivative equals itself. You'll almost exclusively use log base e, and exponentials with a base e in calculus, except when given a different base. In which case, you'll use the change-of-base rule to translate log base b (x) to ln(x)/ln(b), and b^x to e^(ln(b)*x). Exponentials in general have a derivative that is proportional to the original function, but only e^x has this special property. 2^x for instance, has a derivative of ln(2)*2^x.
Second question: I'm not seeing either 12 or 5 in the question you timestamped. Perhaps you have another timestamp in mind. Your notation is confusing, and could use parentheses to add clarity. Assuming you meant 5^(log_5 (12)), where log_5 (12) indicates log base 5 of 12, here's how I would simplify it: Let the expression equal A: 5^(log_5 (12) ) = A Tale the log base 5 of both sides. log_5 ( 5^(log_5 (12) )) = log_5 (A) log_5 (5^x) = x, cancelling out the nested functions that are each others' inverses. Thus: log_5 (12) = log_5 (A) Notice that we have log base 5 as the function on both sides? Since log is a 1-to-1 function for positive real numbers, this means we can equate the arguments. 12 = A Thus, the expression simplifies to 12.
Thank you for the useful video sir. I have one suggestion that could improve the clarity of the lesson: it might be useful to explain why the log rules make sense by describing them in terms of the multiplacation of algebraic bases with exponents. I find that the place where most middle-school maths curriculums fall short is at explaining WHY we use specific formulas and how they were derived.
sir please make daily videos for maths , your explanation is soo perfect sir , your square root finding methods are soo innovative , please upload daily videos , i am ready to watch each and evry video of yours .
You have the rule backwards. log(x)/log(y) does not equal log(x - y). It is log base y of x, since the ratio of logs is the change-of-base rule. The rule you are thinking of, is the difference of logs, equals the log of the ratio. log(x) - log(y) = log(x/y) This equation is still valid, regardless of which logarithmic base we use, as long as we are consistent. You can check that: log(7) - log(2) will indeed be the same as log(7/2)
I love watching your videos even though I have no hope of ever fully comprehending them however, I love to see the power of numbers. Oftentimes in math class students would ask what the point of some math was or how would it be used in real life. Could you post some videos and show how certain people in certain fields do real life applications of the formulas that have or will impact our daily lives. Or show if someone wants to pursue a certain career what they will have to understand. Thanks. Keep up the great work.
Mr. H, I am a mathematics teacher and I love how you teach mathematics without stress. Please never stop helping the world mathematically
Thank you for the encouraging words.
I appreciate it.
Thank you YT teacher
I’m learning more advanced math that my school would not offer to me right now. I just want to say that your videos are incredibly helpful in my advanced math journey.
Great to hear! Thank you.
Fantastic how you explain math. I wish you were there when I was a student. Thank you and keep it up!
Thanks, will do!
It's interesting, and it's funny that in school we used logs to find the answer to a complicated multiplication by adding them and not the other way round as in this video.
We also used slide rules that worked because of their logarithmic scale.
You are absolutely different teacher try some more related with trigonometry identity
Doubt from 1st lecture -- 1. What is log e , give examples
2. I didn't understood 5^log5¹² =12 in 4:28
I Am class 8 th student of india but still almost the whole 1st lecture
Thank you so much sir
You are best teacher I have ever seen
First question:
log base e, or natural log or ln(x) is a special case of a logarithm base. The e stands for Euler's number, which is about 2.71828. Euler's number is a transcendental number like pi, where it is has a never ending or repeating decimal expansion, and where it cannot be calculated with a finite combination of arithmetic, powers, and roots. It is usually a series or a limit that you can use to calculate it.
ln(x) = y, is how you solve the equation A = e^x for x, where A is a number you know, e is a standard constant, and x is a number you don't know.
The reason we are interested in this, is that e^x has special properties in calculus, where its derivative equals itself. You'll almost exclusively use log base e, and exponentials with a base e in calculus, except when given a different base. In which case, you'll use the change-of-base rule to translate log base b (x) to ln(x)/ln(b), and b^x to e^(ln(b)*x).
Exponentials in general have a derivative that is proportional to the original function, but only e^x has this special property. 2^x for instance, has a derivative of ln(2)*2^x.
Second question:
I'm not seeing either 12 or 5 in the question you timestamped. Perhaps you have another timestamp in mind.
Your notation is confusing, and could use parentheses to add clarity. Assuming you meant 5^(log_5 (12)), where log_5 (12) indicates log base 5 of 12, here's how I would simplify it:
Let the expression equal A:
5^(log_5 (12) ) = A
Tale the log base 5 of both sides.
log_5 ( 5^(log_5 (12) )) = log_5 (A)
log_5 (5^x) = x, cancelling out the nested functions that are each others' inverses. Thus:
log_5 (12) = log_5 (A)
Notice that we have log base 5 as the function on both sides? Since log is a 1-to-1 function for positive real numbers, this means we can equate the arguments.
12 = A
Thus, the expression simplifies to 12.
@@carultch ☺️🙏♥️
@@carultch thanks 🙏👍
@@carultch actually the timestamp is of 1st lecture
best math tutor ever
Very useful, thanks
Thanks sir
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Thank you for all the nice comments.
I wish we had lessons on differentiation, calculus...i barely passed maths in school in final year😢
Check out "The organic chemistry tutor"s videos on calculus and pre-calculus. They are very clear and good 💕
Thanks a lot and keep on doing what you're doing..
Your lessons are really helpful...❤
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Understood very easily sir great!! looking forward to 3rd lecture thankyou
Thank you for the useful video sir. I have one suggestion that could improve the clarity of the lesson: it might be useful to explain why the log rules make sense by describing them in terms of the multiplacation of algebraic bases with exponents. I find that the place where most middle-school maths curriculums fall short is at explaining WHY we use specific formulas and how they were derived.
Nice explanation professor 👍 Helped bye interesting examples!
sir please make daily videos for maths , your explanation is soo perfect sir , your square root finding methods are soo innovative , please upload daily videos , i am ready to watch each and evry video of yours .
So good, thank you for this essential knowledge
Another good video.
Glad you enjoyed it
teacher thank you
Hello, Mr.H. I Absolutely love all of your contents. may you please, teach about Combinatorics? I'd love to spend time with it all day.
Thank you so much sir : i just found your channel and love it.
Could you do a playlist series for K.A STROUD: ENGINEERING MATHEMATICS
logs are straightforward however I would not call them laws but rules of Logs because there are no unlawful consequences if not followed
Thank you for your excellent teaching. Kindly help to understand that if logx/logy = log(x-y), then why can not log7/log2 is not equal to log5
You have the rule backwards.
log(x)/log(y) does not equal log(x - y). It is log base y of x, since the ratio of logs is the change-of-base rule.
The rule you are thinking of, is the difference of logs, equals the log of the ratio.
log(x) - log(y) = log(x/y)
This equation is still valid, regardless of which logarithmic base we use, as long as we are consistent.
You can check that:
log(7) - log(2) will indeed be the same as log(7/2)
👌👌👌👌👌
Great review!
❤
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Nice!
Thank u sir
Can you make a video about vectors?
I love watching your videos even though I have no hope of ever fully comprehending them however, I love to see the power of numbers. Oftentimes in math class students would ask what the point of some math was or how would it be used in real life. Could you post some videos and show how certain people in certain fields do real life applications of the formulas that have or will impact our daily lives. Or show if someone wants to pursue a certain career what they will have to understand. Thanks. Keep up the great work.
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Follow Let's Learn Reasoning with Annu for improving reasoning like a pro...👈👈
a reason why i like asians better
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