What is ln(1/((sqrt(2))/2))-ln(1) ?

The solution to ln(1/((sqrt(2))/2))-ln(1) is 1/2 ln(2)

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

simplify

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

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

Decimal Notation

0.34657 \dots

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

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

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

Factor out common term

ln (2)

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

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

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

Apply rule

- (- a) = a

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

2 (6) - 12 ln (2 (6))

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