What is ln(1/(sqrt(2pix^{2n))}) ?

The solution to ln(1/(sqrt(2pix^{2n))}) is -ln(sqrt(2)sqrt(pix^{2n)})

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simplify ln(1/(sqrt(2pix^{2n))})

simplify

ln (\frac{1}{2 π x ^{2 n}})

- ln (2 π x^{2 n})

Solution steps

ln (\frac{1}{2 π x ^{2 n}})

Apply log rule:

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

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

= ln (1) - ln (2 π x^{2 n})

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2 π x^{2 n})

2 π x^{2 n} = 2 π x^{2 n}

= 0 - ln (2 π x^{2 n})

0 - ln (2 π x^{2 n}) = - ln (2 π x^{2 n})

= - ln (2 π x^{2 n})

- lo g_{10} (11.58 \cdot 1 0^{- 5})

lo g_{2} (8 e^{+ 9})

ln (\frac{1 + e ^{x + 2 y}}{e ^{x + 2 y}})

\frac{1}{3} ln (\frac{9 x ^{2} - 16 + 3 x}{4}) + C

ln (20000 \cdot 10000)

What is ln(1/(sqrt(2pix^{2n))}) ?
The solution to ln(1/(sqrt(2pix^{2n))}) is -ln(sqrt(2)sqrt(pix^{2n)})