why is ln e^2x = 2??

Answer 1

ln e^(2x) = 2x ln e = (2x) (1) = 2x

Answer 2

ln (natural log) has a base of e. So when you take the natural log of e (lne) you get 1. Because e is raised to the 2x, you now have 2=2x. This means that x must equal 1.

Answer 3

ln e^2x should equal 2x
since the natural log has a base of e, if you raise e to an exponent, then ln (e^k)=k where k is an arbitrary number.

If x=1, then ln e^2x=2(1)=2

Answer 4

Hi,

Okay, when you have e^2x = 2, we need to get rid of the exponent which is in fact a whole entire expression in itself. We therefore need to take the natural log of both sides of the equation. When we do this, the exponent comes out in front of the ln to get:

2x ln (e) = ln(2)

Now, remember ln(e) equals 1. So therefore, we have:

2x = ln(2)

Next, to get x alone, we need to divide by 2 on both sides of the equation to get:

x = ln(2) / 2 <==== FINAL ANSWER

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 5

im guessing you mean ln(e^(2*x)). That is not equal to 2, but it is equal to 2x.

The reason is that in general, log_b(P^Q) = Q * log_b(P). In words, the base b log of (P to the Q) is equal to Q multiplied by the base b log of P. Here, P is e, our base b is also e, and Q = 2x.

So then ln(e^(2x)) = 2x * ln(e), but ln(e) = 1 because in general, the base b log of b = 1, i.e., log_b(b) = 1.

So then ln(e^(2x)) = 2x * ln(e) = 2x

Hope this helps.

Answer 6

Actually, ln(e^2x) should equal 2x. I guess in your case x=1.

First: ln(a^b) = b*ln(a); so you have 2x*ln(e). But ln(e) = 1.

Because it ln(a)=b means e^b=a. So if you let ln(e)=n, you're saying e^n=e. n must be 1.

Answer 7

ln (e^(2x)) = 2x

I think you meant 2x.

Natural log (ln) is the inverse function to raising something upon the base e.

Similarly common log base 10 (log) is the inverse function to raising something upon the base 10.

log (10^(2x)) would also equal 2x.

Notice, reversing the functions will also work:
e^(ln (2x)) = 2x
10^(log(2x)) = 2x

Answer 8

ln undoes e
ln(e ^ something) = something.

ln (e ^ 2x) = 2x

similarly, e undoes ln

e ^ ln(something) = something.