What is ln?

Ln or "lawn" is the Natural Logarithm which works just like any other log you've learned about, only the base of the natural logarithm is euler's constant (e).
It's often used in questions that involve population growth, bacterial growth, or decay.
Don't get intimidated by this two-letter concept, if you understand logarithms, you're good to go!

[zac]

I have looked at countless websites and countless videos trying to find someone who would explain what natural logs are useful for. This was such a concise and simple explanantion, "natural logs are good for exponential growth".

[infamoushax]

Thank you for this, this saved me so many brain cells

[ian_edits_]

I cannot believe it has taken me two years and countless youtube videos for someone to tell me ln is just loge. everyone always said it like "ln always has base e, it's like log but it always has base e, and they don't have to write it because that's just how it works." Like, yeah, but that's unnecessarily confusing

[beefy]

When your teacher is so incompetent in an hour lesson that you can learn the exact same thing on youtube in a twelfth of the time

[-Brandon]

Arnold, come back to YouTube. We miss you, bud :(

[alakrb]

Thank you so much for explaining this to me.❤

[davidvaquerano]

What an Amazing teacher! Above and beyond the standard

[pwsk]

Please come up with new videos, you are amazing! You explained quite well in this video!

[vishwamanthangyan]

Arnold you're such great tutor, your video help me a lot to understand logarithm.... Thank you

[ik_]

Thanks dear..
I'm from India 🇮🇳❤

[DragonKing]

nice straight forward explanation, thanks!

[bowbookbike]

Thanks so much! I missed three days of algebra class and I come back to this? I was so confused.

[meowplays]

Wow nice video.Easy explanation.❤️From🇧🇩

[nicholascrews]

This was great, but I think it missed something key I see a lot of people get wrong. ln(x) is NOT multiplication of ln*x. The parentheses mean something different here, they mean FUNCTION. Just like f(x) or sqrt(x) mean "plug a value x into this [maybe complicated] black box and it gets transformed into another value", ln(x) means the same thing. One thing I see often is people thinking they can refactor 2ln(x) to ln(2x), but these two aren't equal! Just like 2f(x) != f(2x) and 2sqrt(x) != sqrt(2x).

[natnaelhadishalem]

yoooouuu!! Finally understood some math.

[joesizlack]

I was extremely confused so I watched your video which confused me further, so I input 1 in my homework hoping to get an explanation of why that's the wrong answer, but it was right 🤷‍♂️

[gurpreet]

Thanks, never understood the concept till now.

[riyazveero]

thanks a lot, this came in clutch before my exams lmao

[vusar]

Thank you for this video, it's the best

[eyeofregret]

thanks bro, basically ln(x) = log(x)/log(e) since loge(x)