What is (100)/(2*pi*200)*ln((4+2*200^2)/(25)) ?

The solution to (100)/(2*pi*200)*ln((4+2*200^2)/(25)) is (ln(80004)-2ln(5))/(4pi)

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simplify (100)/(2pi200)ln((4+2200^2)/(25))

simplify

\frac{100}{2 \cdot π \cdot 200} \cdot ln (\frac{4 + 2 \cdot 20 0 ^{2}}{25})

\frac{ln ( 80004 ) - 2 ln ( 5 )}{4 π}

Decimal Notation

0.64226 \dots

Solution steps

\frac{100}{2 π 200} ln (\frac{4 + 2 \cdot 20 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 20 0 ^{2}}{25}) = ln (4 + 2 \cdot 20 0^{2}) - ln (25)

= \frac{100}{2 \cdot 200 π} (ln (20 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 20 0 ^{2} ) - ln ( 25 ) )}{2 π 200}

ln (4 + 2 \cdot 20 0^{2}) = ln (80004)

= \frac{100 ( ln ( 80004 ) - ln ( 25 ) )}{2 \cdot 200 π}

Multiply the numbers:

2 \cdot 200 = 400

= \frac{100 ( ln ( 80004 ) - ln ( 25 ) )}{400 π}

Cancel the common factor:

100

= \frac{ln ( 80004 ) - ln ( 25 )}{4 π}

ln (25) = 2 ln (5)

= \frac{ln ( 80004 ) - 2 ln ( 5 )}{4 π}

ln (\frac{x + x ^{2} - 4}{2})

ln (- 3 e^{2 x})

\frac{1}{3} lo g_{4} (y) - 3 lo g_{4} (x)

ln (\frac{7}{382})

\frac{1}{5} (ln (10 + 101) - ln (- 5 + 26))

What is (100)/(2*pi*200)*ln((4+2*200^2)/(25)) ?
The solution to (100)/(2*pi*200)*ln((4+2*200^2)/(25)) is (ln(80004)-2ln(5))/(4pi)