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

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

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

simplify

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

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

Decimal Notation

- 0.34657 \dots

Solution steps

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

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 (1)

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

ln (1) = 0

= \frac{1}{2} ln (2) - ln (2) - 0

Add similar elements:

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

= - \frac{1}{2} ln (2) - 0

- \frac{1}{2} ln (2) - 0 = - \frac{1}{2} ln (2)

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

ln (8) - 3 ln (\frac{1}{2})

ln (303625 x^{2013176})

ln (a) - 4 ln (b) + 6 ln (c)

ln (0.89 \cdot 1 0^{- 14})

3 lo g_{b} (x) + lo g_{b} (2 y) - 1

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