"ln x = 2"

[master_q 0]

Most trivia chat room sessions I throw in a couple of random questions. Today in our 12th Star Trek trivia session one of the random questions I asked was:

 

(Solve for x) ln x = 2

 

It seemed that no one knew what the answer was so I gave the answer:

 

Answer: x = e^2

 

Then I asked if anyone know logs. Someone then complained that the question was not a log question, but a trig question and that it was one of the many trig functions.

 

Indeed there are trig questions that may require the use of logarithmic functions, but that is just a build up of the use of different mathematics. And the question I asked was not meant to have any connection to trig. And no one is denying that e^x is the only function having a rate of growth equal to its size. And itdoes have connections to other constants and trig like the very famous equation: e^(i * pi) + 1 = 0

 

Whats the connection to trig?

e^(ix) = cos x + i sin x

Which means . . .

ix = ln (cos x + i sin x)

 

And the cool thing is if x equals pi then we get e^(i * pi) + 1 = 0

 

No one is denying this.

e is one of those great #s that has many connections and many interlinking between all the great branches of math, but the idea that my question was a trig question is absolutely false and makes no sense.

 

 

One of the most common definition of e is with (1+1/n)^n. When n approaches infinity (1+1/n)^n approaches e.

 

e = 2.718281828459045235360287471352662497757247093699959574966967628 . . .

 

 

For those that don't know calculus:

 

Think of n getting bigger and bigger . . .

Like if n = 1 then the answer would turn out to be 2

[(1+1/1)^1 = 2]

If n = 2 then we get 2.25

If n = 1,000 then the answer is about 2.716923

If n = 1,000,000 then the answer is about 2.71828

If n = infinity then the answer is about 2.718281828459

(If you look at the above you see the bigger # we put in the closer we get to e)

 

(We could also look at e as summation notation, but that' a another story and the notation will be harder to demonstrate.)

 

 

Back to the question I asked

(Solve for x) ln x = 2

 

ln x = 2 {Reads: natural log of x equals 2)

Means the same as . . .

 

log_e x = 2 {Reads: log base e of x equals 2)

This means . . .

e^2 = x

(e^2 is about 7.38905609)

 

 

It really was as simple as that. There is nothing more to it then that. Let's not make my question more complex then what it really was.

 

 

 

Master Q

StarTrek_Master_Q@yahoo.com

[Ace 0]

Arg!! I could've gotten that! When I read it in the chat, I thought it said "solve for X In (as in the word "in") x = 2." I guess that can happen when you're going fast-paced, and in the chat's font, the uppercase I and lower case l are the same. I'll pay more attention to that next time.

 

erm,,, sorry. I just felt like explaining that. :blink:

[master_q 0]

That's ok. Anyone could have made that mistake.

 

 

Master Q

StarTrek_Master_Q@yahoo.com