What is 2ln((sqrt(2))/2) ?

The solution to 2ln((sqrt(2))/2) is -ln(2)

Popular >

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

simplify

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

- ln (2)

Decimal Notation

- 0.69314 \dots

Solution steps

2 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)

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

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

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

Simplify

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= - ln (2) \cdot 1

Multiply:

ln (2) \cdot 1 = ln (2)

= - ln (2)

lo g_{4} (16 a)

2 lo g_{10} (5) + 5 lo g_{10} (x)

lo g_{b} (\frac{1}{y})

lo g_{3} (x + 4) + lo g_{3} (x - 2)