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Popular >

simplify 4ln((sqrt(2))/2)

Solution

simplify

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

Solution

- 2 ln (2)

+1

Decimal Notation

- 1.38629 \dots

Solution steps

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

Apply log rule:

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

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

= 4 (ln (2) - ln (2))

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

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

Simplify

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{1 \cdot 4}{2} = 2

= - 2 ln (2)

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Frequently Asked Questions (FAQ)

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