What is (800(1/60))/(2pi(15-12))ln(10/2) ?

The solution to (800(1/60))/(2pi(15-12))ln(10/2) is (20(ln(10)-ln(2)))/(9pi)

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simplify (800(1/60))/(2pi(15-12))ln(10/2)

simplify

\frac{800 ( \frac{1}{60} )}{2 π ( 15 - 12 )} ln (\frac{10}{2})

\frac{20 ( ln ( 10 ) - ln ( 2 ) )}{9 π}

Decimal Notation

1.13844 \dots

Solution steps

\frac{800 ( \frac{1}{60} )}{2 π ( 15 - 12 )} ln (\frac{10}{2})

Apply log rule:

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

ln (\frac{10}{2}) = ln (10) - ln (2)

= \frac{800 \cdot \frac{1}{60}}{2 π ( 15 - 12 )} (ln (10) - ln (2))

Multiply fractions:

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

= \frac{800 \cdot \frac{1}{60} ( ln ( 10 ) - ln ( 2 ) )}{2 π ( 15 - 12 )}

2 π (15 - 12) = 6 π

= \frac{800 \cdot \frac{1}{60} ( ln ( 10 ) - ln ( 2 ) )}{6 π}

Multiply

800 \cdot \frac{1}{60} (ln (10) - ln (2)) : \frac{40 ( ln ( 10 ) - ln ( 2 ) )}{3}

= \frac{\frac{40 ( l n ( 10 ) - l n ( 2 ) )}{3}}{6 π}

Apply the fraction rule:

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

= \frac{40 ( ln ( 10 ) - ln ( 2 ) )}{3 \cdot 6 π}

Multiply the numbers:

3 \cdot 6 = 18

= \frac{40 ( ln ( 10 ) - ln ( 2 ) )}{18 π}

Cancel the common factor:

2

= \frac{20 ( ln ( 10 ) - ln ( 2 ) )}{9 π}

ln (\frac{x}{27})

lo g_{7} (\frac{14 x ^{7} y ^{2}}{z ^{14}})

lo g_{5} (\frac{x}{2})

- \frac{1}{921} \cdot ln (\frac{0.01}{100})

- \frac{5}{2} ln (\frac{20}{55})

What is (800(1/60))/(2pi(15-12))ln(10/2) ?
The solution to (800(1/60))/(2pi(15-12))ln(10/2) is (20(ln(10)-ln(2)))/(9pi)