A logarithm formula involving the mascheroni constant

[Kruidnootje]

After watching this video:
The mystery of 0.577

[YOUTUBE]4k1jegU4Wb4[/YOUTUBE]

My problem is at position 7 mins 26 secs where he states the following:
1 - Ln = 1
1+ 1/2 - Ln2 = 0.81
1 + 1/2 + 1/3 - Ln3 = 0.73
And so on until we arrive at Eulers Mascheroni Constant

Being that he is using 'Ln' have learned this is the Natural Logarithm, e, being 2.718. This reads to me as 1.5 minus 2.718 to the power of 2? I spent hours learning about logarithms but this confuses me. Log simply means power is what I learned.

Log 3 means what power does 3 need to be raised to in order to get a specific number, is what I understand. And log simply means 'power' as in 3*3*3*3*3 and so on.
But Natural log 3 makes no sense to me even though I do understand the principle behind 'e'.

I am teaching myself maths, have no college or tutors to turn to; and a maths forum after so many months is my last resort for help. So I would be so grateful.

Sorry folks this is a late edit. I have solved it, thanks to about he 20th you tube video, actually I see now that the light came on when a certain person said ..." what e do I have to raise the power to to get 2, then 3 and so on. But explaining this on a calculator I could see what was happening.

 

[HOI]

After watching this video:
The mystery of 0.577
My problem is at position 7 mins 26 secs where he states the following:
1 - Ln = 1

You mean 1- Ln(1)= 1. That is true because Ln(1)= 0.

1+ 1/2 - Ln2 = 0.81

Ln(2)= 0.69 (to two decimal places) so this is 1+ .5- .69= 1.5- .69= .81 (again, to two decimal places).

1 + 1/2 + 1/3 - Ln3 = 0.73

Ln(3)= 1.10 so this is 1+ .5+ .33- 1.10= 1.83- 1.10= .73 (again, to two decimal places.

And so on until we arrive at Eulers Mascheroni Constant

Yes, of course, that is exactly the definition of the "Euler-Mascheroni" constant.

Being that he is using 'Ln' have learned this is the Natural Logarithm, e, being 2.718. This reads to me as 1.5 minus 2.718 to the power of 2? I spent hours learning about logarithms but this confuses me. Log simply means power is what I learned.

Log 3 means what power does 3 need to be raised to in order to get a specific number, is what I understand. And log simply means 'power' as in 3*3*3*3*3 and so on.
But Natural log 3 makes no sense to me even though I do understand the principle behind 'e'.

I am teaching myself maths, have no college or tutors to turn to; and a maths forum after so many months is my last resort for help. So I would be so grateful.

Sorry folks this is a late edit. I have solved it, thanks to about he 20th you tube video, actually I see now that the light came on when a certain person said ..." what e do I have to raise the power to

"what power do you have to raise e to"

to get 2, then 3 and so on. But explaining this on a calculator I could see what was happening.

 

[Kruidnootje]

="what power do you have to raise e to"

Hallo, thankyou for your reply. To answer your question:

Taking 1+1/2 - Ln2
raising e (2.718) to the power of 2 = 0.69314
Then 1.5 - 0.69314 = 0.80686

That's how I did this, consequently e then raised to the power of 3 and so on. I am teaching myself, somewhat painfully, but of course I am always going to be thankful for corrections and filling in the gaps where I lack understanding. Thankyou for your feedback. Kindest regards.

 

[MarkFL]

Just to clarify, what we have is:

If $e^x=2$, then $x=\ln(2)$. We don't have $e^2=\ln(2)$. :)

The natural log of a number is equal to the power we must raise $e$ to get that number.

 

[Kruidnootje]

Just to clarify, what we have is:

If $e^x=2$, then $x=\ln(2)$. We don't have $e^2=\ln(2)$. :)

The natural log of a number is equal to the power we must raise $e$ to get that number.

Hallo, I really don't grasp at all these last two equations. The first one yes because I have that in my notes. I am not a mathematician nor have I studied maths so please forgive my ignorance, I am more of a visual thinker and I have to be able to visualise in order to understand, abstract thinking has always been a problem with me. However I am progressing, and determined to grasp as much as I can.

Secondly, I thought Log was just a medieval term for 'power' coined by John Napier? So the natural power of a number is equal to the power we must raise e to to get that number.

 

[HOI]

Hallo, thankyou for your reply. To answer your question:

Taking 1+1/2 - Ln2
raising e (2.718) to the power of 2 = 0.69314

NO! e^2= 2.718...^2= 7.38905...
You should have seen that, since e is larger than 2, e^2 is larger than 4.

What you mean is that e to the power of 0.69314 is 2, not the other way around.
That's why ln(2)= 0.69314.

Then 1.5 - 0.69314 = 0.80686

That's how I did this, consequently e then raised to the power of 3 and so on. I am teaching myself, somewhat painfully, but of course I am always going to be thankful for corrections and filling in the gaps where I lack understanding. Thankyou for your feedback. Kindest regards.

Again, ln(3) is NOT "e raised to the power of 3" it is the value of x such that e^x= 3.

 

[Kruidnootje]

Ok got it. Made many a mistake. But the light is on. Thanks.