1. Simplify the following expressions:

   1. \(\ln{x}+\ln{y}\)

   2. \(\ln{a}-\ln{b}\)

   3. \(2\ln{f}+3\ln{f}\)

   4. \(e^{m}e^{k}\)

   5. \(\frac{e^{c}}{e^{d}}\)

2. Expand the following expressions:

   1. \(e^{(3h-j)}\)

   2. \(e^{2(c+w)}\)

   3. \(\ln{h/g}\)

   4. \(\ln(kT)\)

   5. \(\ln{\sqrt{\frac{q}{r}}}\)