Question

how to take log of \[\beta ^{\alpha}(1+(x/\beta)^{\alpha})^{2}\]?

Answer 1

\[\beta ^{\alpha}(1+(x/\beta)^{\alpha})^{2}\]

Answer 2

\[ \log[\beta^\alpha (1+ (x/\beta)^\alpha)^2] = \log[\beta^\alpha] + \log[(1+(x/\beta)^\alpha)^2] \]
\[ = \alpha\log[\beta] + 2\log[1+(x/\beta)^\alpha]\]