Why do we get rid of the $-$ sign in this equation I am finding interquartile ranges for the exponential function cdf as part of a project for university:
$$Q\left(\frac{1}{4}\right) = -\frac{1}{\lambda}\ln\left(1-\frac{1}{4}\right)= -\frac{1}{\lambda}\ln\left(\frac{3}{4}\right)=  \frac{1}{\lambda}\left(\ln(4) - \ln(3)\right)$$ I do understand the quotient rule of logarithm but the rule states that if I have $\ln(\frac{3}{4})$ this should be the same as $\ln(3) - \ln(4)$ but in the above case is $\ln(4)-\ln(3)$, furthermore, where did the $(-)$ sign go at the end of the equation for $\frac{1}{\lambda}$? what am I missing?

A minus sign switches the order of subtraction: ${-}(a-b) = b-a$.  You can see this by writing ${-}(a-b)$ as ${-}(a + {-}{-}b)$ and distributing the negative:  ${-}(a-b) = {-}(a + {-}b) = -a + {-}{-}b = b -a$.
Alternatively: Use the identity ${-}\ln(x) = \ln(1/x)$.
