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Popular >

simplify-1/(sqrt(2))ln(1/(sqrt(2)))+1/(sqrt(2))

Solution

simplify

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

Solution

\frac{2}{4} ln (2) + \frac{2}{2}

+1

Decimal Notation

0.95217 \dots

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

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

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

Apply rule

- (- a) = a

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

ln (2) \frac{1}{2 2} = \frac{2}{4} ln (2)

\frac{1}{2} = \frac{2}{2}

= \frac{2}{4} ln (2) + \frac{2}{2}

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Frequently Asked Questions (FAQ)

What is simplify-1/(sqrt(2))ln(1/(sqrt(2)))+1/(sqrt(2)) ?
The solution to simplify-1/(sqrt(2))ln(1/(sqrt(2)))+1/(sqrt(2)) is (sqrt(2))/4 ln(2)+(sqrt(2))/2