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simplificar (4pi10^{-7}10(0.2))/(2pi)[ln(0.18)-ln(0.08)]

Solução

simplificar

\frac{4 π \cdot 1 0 ^{- 7} \cdot 10 ( 0.2 )}{2 π} [ln (0.18) - ln (0.08)]

\frac{1}{2500000} ln (2.25)

Decimal

3.24372 E - 7

Passos da solução

\frac{4 π 1 0 ^{- 7} \cdot 10 ( 0.2 )}{2 π} [ln (0.18) - ln (0.08)]

Aplicar as propriedades dos logaritmos:

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

ln (0.18) - ln (0.08) = ln (\frac{0.18}{0.08})

= \frac{1 0 ^{- 7} \cdot 4 \cdot 10 \cdot 0.2 π}{2 π} [ln (\frac{0.18}{0.08})]

Dividir:

\frac{0.18}{0.08} = 2.25

= \frac{4 π 1 0 ^{- 7} \cdot 10 \cdot 0.2}{2 π} [ln (2.25)]

Remover os parênteses:

(a) = a

= \frac{4 π 1 0 ^{- 7} \cdot 10 \cdot 0.2}{2 π} ln (2.25)

Multiplicar frações:

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

= \frac{4 π 1 0 ^{- 7} \cdot 10 \cdot 0.2 ln ( 2.25 )}{2 π}

Eliminar o fator comum:

π

= \frac{4 \cdot 1 0 ^{- 7} \cdot 10 \cdot 0.2 ln ( 2.25 )}{2}

Multiplicar os números:

4 \cdot 10 \cdot 0.2 = 8

= \frac{1 0 ^{- 7} \cdot 8 ln ( 2.25 )}{2}

Dividir:

\frac{8}{2} = 4

= 1 0^{- 7} \cdot 4 ln (2.25)

Aplicar as propriedades dos expoentes:

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

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

= 4 \cdot \frac{1}{1 0 ^{7}} ln (2.25)

Multiplicar frações:

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

= \frac{1 \cdot 4}{1 0 ^{7}} ln (2.25)

\frac{1 \cdot 4}{1 0 ^{7}} = \frac{1}{2500000}

= \frac{1}{2500000} ln (2.25)

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