use properties of logarithms to expand the logarithmic expression as much as possilbe. Evaluate logarithmic expressions without using a calculator if possible. ln(e^5/5)= Solution Given : ln {(e^5)/5} To expand we use following log properties: ln(x*y/z) = lnx +lny - lnz So, ln {(e^5)/5} = ln(e^5) -ln(5) Now we use the property : ln(a^x) = x*lna So, ln {(e^5)/5} = ln(e^5) -ln(5) = 5ln(e) - ln(5) Now lne = lnee = lne/lne =1 So,ln {(e^5)/5} = ln(e^5) -ln(5) = 5ln(e) - ln(5) = 5 - ln5 (simplified form ).