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

Globokim8

Globokim8

Answered question

2021-11-09

Find the exact value of the logarithmic expression ln(1e) without using a calculator.If this is not possible, state the reason.

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2021-11-10Added 108 answers

Step 1 
Given: 
Let y=ln(1e) 
To Find:To assess the provided 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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