## JohnT 3 years ago 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?

1. JohnT

$\ln \left( \sec x \right) = - \ln \left( \cos x \right)$

2. hartnn

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

3. JohnT

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

4. hartnn

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