Question

Does ln(sec(x)) = - ln(cos(x)) ? The graphs look the same, but if I gave this answer on a test, would it be accurate?

Answer 1

\[\ln \left( \sec x \right) = - \ln \left( \cos x \right)\]

Answer 2

yes, it is same
\(\ln (1/a)= \ln (a^{-1})= -\ln a \)
here, a = cos x = 1/ sec x, right ?

Answer 3

Ah, I see. Your equation with the power example makes sense.

Answer 4

to be more accurate, i'll suggest you to write :
\(-\ln|\cos x| \)
because log of negative numbers is not defined...