What is (3*4pi*10^{-7})/(2pi)ln(10/5) ?

The solution to (3*4pi*10^{-7})/(2pi)ln(10/5) is 3/5000000 (ln(10)-ln(5))

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simplify (34pi10^{-7})/(2pi)ln(10/5)

simplify

\frac{3 \cdot 4 π \cdot 1 0 ^{- 7}}{2 π} ln (\frac{10}{5})

\frac{3}{5000000} (ln (10) - ln (5))

Decimal Notation

4.15888 E - 7

Solution steps

\frac{3 \cdot 4 π 1 0 ^{- 7}}{2 π} ln (\frac{10}{5})

Apply log rule:

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

ln (\frac{10}{5}) = ln (10) - ln (5)

= \frac{1 0 ^{- 7} \cdot 3 \cdot 4 π}{2 π} (ln (10) - ln (5))

Multiply fractions:

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

= \frac{3 \cdot 4 π 1 0 ^{- 7} ( ln ( 10 ) - ln ( 5 ) )}{2 π}

Cancel the common factor:

π

= \frac{3 \cdot 4 \cdot 1 0 ^{- 7} ( ln ( 10 ) - ln ( 5 ) )}{2}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{1 0 ^{- 7} \cdot 12 ( ln ( 10 ) - ln ( 5 ) )}{2}

Divide the numbers:

\frac{12}{2} = 6

= 1 0^{- 7} \cdot 6 (ln (10) - ln (5))

Apply exponent rule:

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

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

= 6 \cdot \frac{1}{1 0 ^{7}} (ln (10) - ln (5))

Multiply fractions:

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

= \frac{1 \cdot 6}{1 0 ^{7}} (ln (10) - ln (5))

\frac{1 \cdot 6}{1 0 ^{7}} = \frac{3}{5000000}

= \frac{3}{5000000} (ln (10) - ln (5))

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (z)

ln (\frac{2 ^{\frac{34}{5}} x ^{15}}{y ^{20}})

ln ((t) (t + 4) (t + 6))

ln (\frac{40}{450})

\frac{1}{2} ln (2 (9.5) + 1) + 2 ln (9.5 - 1)

What is (3*4pi*10^{-7})/(2pi)ln(10/5) ?
The solution to (3*4pi*10^{-7})/(2pi)ln(10/5) is 3/5000000 (ln(10)-ln(5))