e^ln=1???

Mighty Grandiose Noble Knight

1

Hey

I just cannot comprehend this indentity:

e^ln=1 :s-smilie:

Can any mathematician help me out here.

Thanks for the help in advance :yep:

Edit: Oh yeah sorry I just realised it was ln something. How about this e^ln3=3?

wat

a^{log_a(b)} = b

and

ln(x) = log_e(x)

Reply 3

ashy

17

They're inverse processes like sin and arcsin, or multiplication and division. 2 x 2 / 2 = 2. arcsin(sin[x]) = x

Reply 4

Glutamic Acid

17

e^ln makes no sense; the natural logarithm of what? I presume you mean e^(ln 1) = 1. e and ln are inverses, so the operations performed upon 1 cancel out leaving 1.

Reply 5

v-zero

14

That's because it's nonsensical. e^ln(1) = 1 = e^0 .....

'Ln' is a function, not a number. Like Sine or Cosine, it is variable dependent upon what number the function is applied to.

'Ln' is the natural log, the log to the base e. It gives an answer to the question: 'what number would I have to raise e to in order to get this number?'.

Better?

Or e^(i*pi)=-1

Glutamic Acid

e^ln makes no sense; the natural logarithm of what? I presume you mean e^(ln 1) = 1. e and ln are inverses, so the operations performed upon 1 cancel out leaving 1.

This.

@ your sig.

Reply 8

dbmag9

15

I assume the OP means e^(i&#960 :wink:

; it's relatively easy to misread these if you don't know what symbols to expect. It equals -1, which is known as Euler's identity.

Reply 9

Mighty Grandiose Noble Knight

OP

1

matt2k8

a^{log_a(b)} = b

and

ln(x) = log_e(x)

This is what I was on about. Do you have a proof for this or another way of thinking about it?

Reply 10

JMonkey

3

Try:

e\simeq{2.71828183}

log_{2.718281828}\simeq{ln}

e^{ln(x)}=x\;\;\;\;\; if x>0

ln({e^x})=x

Therefore

e^{ln}=1

It's an inverse because they are intimately related in that way. The natural logarithm of a number x is the power to which e would have to be raised to equal x.

Reply 11

Mighty Grandiose Noble Knight

OP

1

v-zero

That's because it's nonsensical. e^ln(1) = 1 = e^0 .....

'Ln' is a function, not a number. Like Sine or Cosine, it is variable dependent upon what number the function is applied to.

'Ln' is the natural log, the log to the base e. It gives an answer to the question: 'what number would I have to raise e to in order to get this number?'.

Better?

Are you saying what x is in the equation e^x=ln?

Reply 12

Mighty Grandiose Noble Knight

OP

1

JMonkey

Try

e\simeq{2.71828183}

log_{2.718281828}\simeq{e}

e^{ln(x)}=x\;\;\;\;\; if x>0

ln({e^x})=x

Therefore

e^{ln}=1

It's an inverse because they are intimately related in that way. The natural logarithm of a number x is the power to which e would have to be raised to equal x.

How is

log_{2.718281828}\simeq{e}

I thought log to the base e was ln?

Reply 13

JMonkey

3

Mighty Grandiose Noble Knight

How is

log_{2.718281828}\simeq{e}

I thought log to the base e was ln?

That's in fact what I meant to say but I didn't edit it quickly enough. I am **** at latex. Apologies.

JMonkey

That's in fact what I meant to say but I didn't edit it quickly enough. I am **** at latex. Apologies.

Use the Preview Post button to check your LaTeX.

Reply 15

JMonkey

3

It's a way of thinking about it. It wasn't meant to be formally correct, obviously that wasn't working but point taken.

He didn't understand the log rules, so it seemed pointless to reiterate the same thing again.

And by the way, you guys might want to give people time to edit, just a suggestion. I am slow k in latex, because I keep ******* it up. :tongue:

Reply 16

JMonkey

3

Mr M

Use the Preview Post button to check your LaTeX.

That's the best piece of advice I've had today. Usually I do but I thought this was simple enough. My bad apologies.

Reply 17

JMonkey

3

Mighty Grandiose Noble Knight

I see lol. Its alright matey we all make mistakes :biggrin:

Thanks for your help.

Lol. for what it was worth ie nothing. :smile:

Reply 18

Mighty Grandiose Noble Knight

OP

1

I understand the above principal 100% but...here's a question:

say g(x)=e^ln3

g(x)=3 yes

But what was g(x) in the first place or could we just let g(x) be a number such as z? If this is the case than I understand it hahaha Thanks for your help.