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

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

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

simplify

ln (\frac{1}{2 \cdot π \cdot x})

- ln (2 π x)

Solution steps

ln (\frac{1}{2 π x})

Apply log rule:

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

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

= ln (1) - ln (2 π x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2 π x)

2 π x = 2 π x

= 0 - ln (2 π x)

0 - ln (2 π x) = - ln (2 π x)

= - ln (2 π x)

lo g_{3} (10) - lo g_{3} (5) lo g_{3} (18)

lo g_{b} (2) + 2 lo g_{b} (x)

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

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

lo g_{10} (5 x) - lo g_{10} (4 y)

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