use properties of logarithms to expand the logarithmic expre

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 = ln_ee = lne/lne =1

So,ln {(e^5)/5} = ln(e^5) -ln(5) = 5ln(e) - ln(5) = 5 - ln5 (simplified form )