What is (300)/(2*pi*450)*ln((4+2*450^2)/(25)) ?

The solution to (300)/(2*pi*450)*ln((4+2*450^2)/(25)) is (ln(405004)-2ln(5))/(3pi)

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simplify (300)/(2pi450)ln((4+2450^2)/(25))

simplify

\frac{300}{2 \cdot π \cdot 450} \cdot ln (\frac{4 + 2 \cdot 45 0 ^{2}}{25})

\frac{ln ( 405004 ) - 2 ln ( 5 )}{3 π}

Decimal Notation

1.02843 \dots

Solution steps

\frac{300}{2 π 450} ln (\frac{4 + 2 \cdot 45 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 45 0 ^{2}}{25}) = ln (4 + 2 \cdot 45 0^{2}) - ln (25)

= \frac{300}{2 \cdot 450 π} (ln (45 0^{2} \cdot 2 + 4) - ln (25))

Multiply fractions:

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

= \frac{300 ( ln ( 4 + 2 \cdot 45 0 ^{2} ) - ln ( 25 ) )}{2 π 450}

ln (4 + 2 \cdot 45 0^{2}) = ln (405004)

= \frac{300 ( ln ( 405004 ) - ln ( 25 ) )}{2 \cdot 450 π}

Multiply the numbers:

2 \cdot 450 = 900

= \frac{300 ( ln ( 405004 ) - ln ( 25 ) )}{900 π}

Cancel the common factor:

300

= \frac{ln ( 405004 ) - ln ( 25 )}{3 π}

ln (25) = 2 ln (5)

= \frac{ln ( 405004 ) - 2 ln ( 5 )}{3 π}

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

- lo g_{10} (4.61 \cdot 1 0^{- 7})

\frac{2 ln ( 3 )}{ln ( 7 )} - 10

lo g_{10} (3 x^{3}) \cdot ln (10)

ln (\frac{11 π}{2})

What is (300)/(2*pi*450)*ln((4+2*450^2)/(25)) ?
The solution to (300)/(2*pi*450)*ln((4+2*450^2)/(25)) is (ln(405004)-2ln(5))/(3pi)