Find the exact value of the logarithmic expression \ln\left(\frac{1}{\sqrt e}

Globokim8 2021-11-09 Answered
Find the exact value of the logarithmic expression ln(1e) without using a calculator.If this is not possible, state the reason.
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Expert Answer

Faiza Fuller
Answered 2021-11-10 Author has 108 answers
Step 1
Given:
Let y=ln(1e)
To Find: To evaluate the given expression.
Step 2
Solution:
y=ln(1e)
We know that  ln(ab)=lnalnb       (Properties of logarithms)
y=ln1ln(e)
Since  ln1=0
y=0ln(e)
y=ln(e)12
We know that  lnxn       (Properties of logarithms)
y=12lne
Since  lne=1
y=12×1
y=12
Hence  ln(1e)=12
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