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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 )

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use properties of logarithms to expand the logarithmic expression as.pdf

  • 1. 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 )