What is ln(1/(sqrt(2*pi*\det(x)))) ?

The solution to ln(1/(sqrt(2*pi*\det(x)))) is -ln(sqrt(2)sqrt(pi\det(x)))

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simplify ln(1/(sqrt(2pi\det(x))))

simplify

ln (\frac{1}{2 \cdot π \cdot det ( x )})

- ln (2 π det (x))

Solution steps

ln (\frac{1}{2 π det ( x )})

Apply log rule:

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

ln (\frac{1}{2 π det ( x )}) = ln (1) - ln (2 π det (x))

= ln (1) - ln (2 π det (x))

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2 π det (x))

2 π det (x) = 2 π det (x)

= 0 - ln (2 π det (x))

0 - ln (2 π det (x)) = - ln (2 π det (x))

= - ln (2 π det (x))

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

ln (x) + ln (x^{2} - 1)

ln (\frac{22.4}{10.1})

ln (x) + 2 ln (8)

3 - ln^{2} ((cos (x))^{\frac{3}{2}})

What is ln(1/(sqrt(2*pi*\det(x)))) ?
The solution to ln(1/(sqrt(2*pi*\det(x)))) is -ln(sqrt(2)sqrt(pi\det(x)))