What is ln(1/((sqrt(2pi)^7))) ?

The solution to ln(1/((sqrt(2pi)^7))) is -7/2 ln(2pi)

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simplify ln(1/((sqrt(2pi)^7)))

simplify

ln \frac{1}{( 2 π ^{7} )}

- \frac{7}{2} ln (2 π)

Decimal Notation

- 6.43256 \dots

Solution steps

ln \frac{1}{( ( 2 π ) ^{7} )}

Apply log rule:

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

ln \frac{1}{( ( 2 π ) ^{7} )} = ln (1) - ln (((2 π)^{7}))

= ln (1) - ln ((2 π)^{7})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((2 π)^{7}) = 7 ln (2 π)

= ln (1) - 7 ln (2 π)

ln (1) = 0

7 ln (2 π) = \frac{7}{2} ln (2 π)

= 0 - \frac{7}{2} ln (2 π)

0 - ln (2 π) \frac{7}{2} = - ln (2 π) \frac{7}{2}

= - \frac{7}{2} ln (2 π)

ln (\frac{20}{9})

3 lo g_{4} (x) + 5 lo g_{4} (y)

- \frac{4}{ln ( 6 ) 5}

\frac{3}{4} \cdot ln (2)

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

What is ln(1/((sqrt(2pi)^7))) ?
The solution to ln(1/((sqrt(2pi)^7))) is -7/2 ln(2pi)