What is simplify-100*10^3*20*10^{-9}ln((10-5)/(10+5)) ?

The solution to simplify-100*10^3*20*10^{-9}ln((10-5)/(10+5)) is (ln(3))/(500)

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simplify-10010^320*10^{-9}ln((10-5)/(10+5))

simplify

- 100 \cdot 1 0^{3} \cdot 20 \cdot 1 0^{- 9} ln (\frac{10 - 5}{10 + 5})

\frac{ln ( 3 )}{500}

Solution steps

- 100 \cdot 1 0^{3} \cdot 20 \cdot 1 0^{- 9} ln (\frac{10 - 5}{10 + 5})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{3} \cdot 1 0^{- 9} = 1 0^{3 - 9}

= - 100 \cdot 20 \cdot 1 0^{3 - 9} ln (\frac{10 - 5}{10 + 5})

Subtract the numbers:

3 - 9 = - 6

= - 100 \cdot 20 \cdot 1 0^{- 6} ln (\frac{10 - 5}{10 + 5})

Apply exponent rule:

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

1 0^{- 6} = \frac{1}{1 0 ^{6}}

= 100 \cdot 20 \cdot \frac{1}{1 0 ^{6}} ln (\frac{10 - 5}{10 + 5})

Multiply fractions:

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

= - \frac{1 \cdot 100 \cdot 20 ln ( \frac{10 - 5}{10 + 5} )}{1 0 ^{6}}

1 \cdot 100 \cdot 20 ln (\frac{10 - 5}{10 + 5}) = 2000 ln (\frac{5}{15})

= - \frac{2000 ln ( \frac{5}{15} )}{1 0 ^{6}}

Cancel

\frac{2000 ln ( \frac{5}{15} )}{1 0 ^{6}} : \frac{ln ( \frac{5}{15} )}{5 ^{3} \cdot 2 ^{2}}

= - \frac{ln ( \frac{5}{15} )}{5 ^{3} \cdot 2 ^{2}}

\frac{5}{15} = \frac{1}{3}

= - \frac{ln ( \frac{1}{3} )}{5 ^{3} \cdot 2 ^{2}}

5^{3} \cdot 2^{2} = 500

= - \frac{ln ( \frac{1}{3} )}{500}

Simplify

ln (\frac{1}{3}) : - ln (3)

= - \frac{- ln ( 3 )}{500}

Apply the fraction rule:

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

= - (- \frac{ln ( 3 )}{500})

Apply rule

- (- a) = a

= \frac{ln ( 3 )}{500}

(3.05 \cdot 1 0^{- 1}) (3 \cdot 1 0^{4})

2 π (100) (10 \cdot 1 0^{- 3})

- 8.75 \cdot 1 0^{- 6}

2.37 \cdot 1 0^{- 13} \cdot \frac{48}{169}

What is simplify-100*10^3*20*10^{-9}ln((10-5)/(10+5)) ?
The solution to simplify-100*10^3*20*10^{-9}ln((10-5)/(10+5)) is (ln(3))/(500)