What is (50*3.5)/(2*pi)*ln((4*1000)/(0.8*1000)) ?

The solution to (50*3.5)/(2*pi)*ln((4*1000)/(0.8*1000)) is (175)/(2pi)(ln(4000)-ln(800))

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simplify (503.5)/(2pi)ln((41000)/(0.8*1000))

simplify

\frac{50 \cdot 3.5}{2 \cdot π} \cdot ln (\frac{4 \cdot 1000}{0.8 \cdot 1000})

\frac{175}{2 π} (ln (4000) - ln (800))

Decimal Notation

44.82624 \dots

Solution steps

\frac{50 \cdot 3.5}{2 π} ln (\frac{4 \cdot 1000}{0.8 \cdot 1000})

Apply log rule:

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

ln (\frac{4 \cdot 1000}{0.8 \cdot 1000}) = ln (4 \cdot 1000) - ln (0.8 \cdot 1000)

= \frac{50 \cdot 3.5}{2 π} (ln (4 \cdot 1000) - ln (1000 \cdot 0.8))

Multiply the numbers:

50 \cdot 3.5 = 175

= \frac{175}{2 π} (ln (4 \cdot 1000) - ln (1000 \cdot 0.8))

Multiply the numbers:

4 \cdot 1000 = 4000

= \frac{175}{2 π} (ln (4000) - ln (1000 \cdot 0.8))

Multiply the numbers:

0.8 \cdot 1000 = 800

= \frac{175}{2 π} (ln (4000) - ln (800))

2 ln (5) - 3 ln (3) + ln (5) - ln (3)

ln (\frac{1 + 4}{2})

ln (2) + 5 ln (x)

ln (e) + ln (2 x) - ln (3 y) - 2 ln (z)

ln (z \frac{y}{z})

What is (50*3.5)/(2*pi)*ln((4*1000)/(0.8*1000)) ?
The solution to (50*3.5)/(2*pi)*ln((4*1000)/(0.8*1000)) is (175)/(2pi)(ln(4000)-ln(800))