What is (4*pi*10^{-7})/(2*pi)*ln(27/16) ?

The solution to (4*pi*10^{-7})/(2*pi)*ln(27/16) is 1/5000000 (3ln(3)-4ln(2))

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simplify (4pi10^{-7})/(2pi)ln(27/16)

simplify

\frac{4 \cdot π \cdot 1 0 ^{- 7}}{2 \cdot π} \cdot ln (\frac{27}{16})

\frac{1}{5000000} (3 ln (3) - 4 ln (2))

Decimal Notation

1.0465 E - 7

Solution steps

\frac{4 π 1 0 ^{- 7}}{2 π} ln (\frac{27}{16})

Apply log rule:

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

ln (\frac{27}{16}) = ln (27) - ln (16)

= \frac{1 0 ^{- 7} \cdot 4 π}{2 π} (ln (27) - ln (16))

Multiply fractions:

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

= \frac{4 π 1 0 ^{- 7} ( ln ( 27 ) - ln ( 16 ) )}{2 π}

Cancel the common factor:

π

= \frac{4 \cdot 1 0 ^{- 7} ( ln ( 27 ) - ln ( 16 ) )}{2}

Divide the numbers:

\frac{4}{2} = 2

= 1 0^{- 7} \cdot 2 (ln (27) - ln (16))

ln (27) = 3 ln (3)

ln (16) = 4 ln (2)

= 1 0^{- 7} \cdot 2 (3 ln (3) - 4 ln (2))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

1 0^{- 7} = \frac{1}{1 0 ^{7}}

= 2 \cdot \frac{1}{1 0 ^{7}} (3 ln (3) - 4 ln (2))

Multiply fractions:

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

= \frac{1 \cdot 2}{1 0 ^{7}} (3 ln (3) - 4 ln (2))

\frac{1 \cdot 2}{1 0 ^{7}} = \frac{1}{5000000}

= \frac{1}{5000000} (3 ln (3) - 4 ln (2))

5 ln (x^{3}) - 2 ln (x^{4})

\frac{1}{4} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

lo g_{4} (\frac{1}{16} x)

2 lo g_{10} (a) + 3 lo g_{10} (b)

lo g_{8} (x z^{3})

What is (4*pi*10^{-7})/(2*pi)*ln(27/16) ?
The solution to (4*pi*10^{-7})/(2*pi)*ln(27/16) is 1/5000000 (3ln(3)-4ln(2))