Question

what is ln(ln2) - ln(ln 1)

Answer 1

ln 1 = 0
and
ln 0 is undefined

Answer 2

so its infinty

Answer 3

in terms of limits the answer is infinity
\[\ln(\ln 2) - \lim_{x \rightarrow 1} \ln(\ln x) = \ln(\ln 2) - (-\infty) = \infty\]

Answer 4

how can i find the value of p
The integral from 1 to 2 of 1/(x(ln(x)^p)) dx
i already Substitute u=ln(x) and you get 1/u^p

Answer 5

\[\int\limits_{1}^{2}\frac{ dx }{ x (\ln x )^{p} }\]

Answer 6

in to \[\int\limits_{1}^{2} \frac{ 1 }{ u ^{p} }\]

Answer 7

how can i find tha value of p to make it converges

Answer 8

\[\int\limits_1^2 u^{-p} du = \frac{u^{1-p}}{1-p} = \frac{(\ln x) ^{1-p}}{1-p}\]
plug in limits

Answer 9

??? no idea

Answer 10

why we divided by 1-p

Answer 11

power rule for integrating a polynomial
\[\int\limits x^n = \frac{x^{n+1}}{n+1}\]

Answer 12

how it acuatlly became u to thepower1-p

Answer 13

aha

Answer 14

that was stupid

Answer 15

as long as p does not equal 1, it will converge because ln(1) = 0

Answer 16

so the value of p should be bigger than 1

Answer 17

p can be any number other than 1

Answer 18

thank you very much you made my day <3

Answer 19

yw