What is (100)/(2*pi*400)*ln((4+2*400^2)/(25)) ?

The solution to (100)/(2*pi*400)*ln((4+2*400^2)/(25)) is (ln(320004)-2ln(5))/(8pi)

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simplify (100)/(2pi400)ln((4+2400^2)/(25))

simplify

\frac{100}{2 \cdot π \cdot 400} \cdot ln (\frac{4 + 2 \cdot 40 0 ^{2}}{25})

\frac{ln ( 320004 ) - 2 ln ( 5 )}{8 π}

Decimal Notation

0.37629 \dots

Solution steps

\frac{100}{2 π 400} ln (\frac{4 + 2 \cdot 40 0 ^{2}}{25})

Apply log rule:

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

ln (\frac{4 + 2 \cdot 40 0 ^{2}}{25}) = ln (4 + 2 \cdot 40 0^{2}) - ln (25)

= \frac{100}{2 \cdot 400 π} (ln (40 0^{2} \cdot 2 + 4) - ln (25))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{100 ( ln ( 4 + 2 \cdot 40 0 ^{2} ) - ln ( 25 ) )}{2 π 400}

ln (4 + 2 \cdot 40 0^{2}) = ln (320004)

= \frac{100 ( ln ( 320004 ) - ln ( 25 ) )}{2 \cdot 400 π}

Multiply the numbers:

2 \cdot 400 = 800

= \frac{100 ( ln ( 320004 ) - ln ( 25 ) )}{800 π}

Cancel the common factor:

100

= \frac{ln ( 320004 ) - ln ( 25 )}{8 π}

ln (25) = 2 ln (5)

= \frac{ln ( 320004 ) - 2 ln ( 5 )}{8 π}

ln (2) - ln (5) - ln (1) + ln (4)

ln (\frac{1}{382})

ln (\frac{72}{129})

ln (\frac{5 w ^{2} v}{x + y})

ln_{e} (x^{\frac{1}{8}})

What is (100)/(2*pi*400)*ln((4+2*400^2)/(25)) ?
The solution to (100)/(2*pi*400)*ln((4+2*400^2)/(25)) is (ln(320004)-2ln(5))/(8pi)