What is log_{e}(2sqrt(2)) ?

The solution to log_{e}(2sqrt(2)) is 3/2 ln(2)

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simplify log_{e}(2sqrt(2))

simplify

lo g_{e} (22)

\frac{3}{2} ln (2)

Decimal Notation

1.03972 \dots

Solution steps

lo g_{e} (22)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{e} (22) = lo g_{e} (2) + lo g_{e} (2)

= lo g_{e} (2) + lo g_{e} (2)

lo g_{e} (2) = ln (2)

lo g_{e} (2) = \frac{1}{2} ln (2)

= ln (2) + \frac{1}{2} ln (2)

Factor out common term

ln (2)

= ln (2) (1 + \frac{1}{2})

1 + \frac{1}{2} = \frac{3}{2}

= \frac{3}{2} ln (2)

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