Question

The value of loge√e=?

Answer 1

The common logarithm value of e can be written as log10e. Thus, common logarithm value of log e = 0.434 (approx.)

Answer 2

$\displaystyle \sf{ log_{e}( \sqrt{e} ) } = \frac{1}{2}$

Given :

$\displaystyle \sf{ log_{e}( \sqrt{e} ) }$

To find :

The value of the expression

Formula Used :

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log_{a}(a) = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ log_{e}( \sqrt{e} ) }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{e}( \sqrt{e} ) }$

$\displaystyle \sf{ = log_{e}( {e}^{ \frac{1}{2} } ) }\: \: \: \bigg[ \: \because \: log( {a}^{n} ) = n log(a)\bigg]$

$\displaystyle \sf{ = \frac{1}{2} log_{e}( {e}^{ } ) }$

$\displaystyle \sf{ = \frac{1}{2} } \times 1\: \: \: \bigg[ \: \because \: log_{a}(a) = 1\bigg]$

$\displaystyle \sf{ = \frac{1}{2} }$

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