Question

why does -8ln|sqrt(2) -1| = 8(ln(1/sqrt(2)-1) ?

Answer 1

Can someone explain or prove this? Thanks

Answer 2

\[-8 \ln \left| \sqrt{2} -1 \right| = 8 \ln \left| \frac{ 1 }{ \sqrt{2} -1 } \right|\]

Answer 3

\[\Large -8 \ln \left| \sqrt{2} -1 \right| = 8\ln \left| (\sqrt{2} -1)^{-1} \right|\]


\[\Large -8 \ln \left| \sqrt{2} -1 \right| = 8 \ln \left| \frac{ 1 }{ \sqrt{2} -1 } \right|\]


I used this rule y*ln(x) = ln(x^y) for step 1


Then I used this rule for step 2: x^(-k) = 1/(x^k)