Logarithm problem?

Question

Why ln(e) =1?

Answer 1

To find the log of a number "n" to the base "b" we have to ask, what power do we have to raise b to to get n. That is if the answer is "x" then b^x = n. or lb(n) = x

If n = b we have n^x = n so x must be 1.

ln means natural log which is a logarithm to the base e,
so we have e^x = e or ln(e) = x so x must be 1.

Answer 2

Ln is the narural log which is base e. Therefore, ln(e)=1 just as log(10)=1. Also, e=e^1 therefore ln(e) = 1.

Answer 3

ln (base b) a = c means a = b^c

ln e = 1 means log (base e) e = 1

that means e^1 = e

Does this make sense?

Answer 4

The number "e" is alled the base of natural logarithms because in a differential equation of the form

dy/dx=Cy

"e^x" is the basic solution you get when you have "natural units" or C=1. The interesting idea is this: you have something which obeys this kind of equation--say y=the amount of a radioactive isotope and x=the time. The constant "C" is then going to have units of 1/seconds. There is no law which requires you to measure time in seconds--in fact, you can use the amount of isotope itself as the clock. This is the "natural" time unit for the problem.

Answer 5

ln means natural log .This is to base e that's why ln(e)=1

Answer 6

it is defined to be that way in means log to the base e

if ln(e) = x the e^x = e that is e^x = e^1 or x =1

Answer 7

A natural fact

Answer 8

ln(e) = 1

the reason why is because they cancel each other out.

Answer 9

because e^1 = e

ln(e^X) = X

ln(Z) = the power to bring e to in order to get Z

so

ln(z) = y, then: e^y = z

Answer 10

It's just one of those laws.