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simplificar-ln(1-(4.5)/5)26610^{-12}*270

Solución

simplificar

- ln (1 - \frac{4.5}{5}) \cdot 266 \cdot 1 0^{- 12} \cdot 270

1.65372 E - 7

Pasos de solución

- ln (1 - \frac{4.5}{5}) \cdot 266 \cdot 1 0^{- 12} \cdot 270

Aplicar las leyes de los exponentes:

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

= - 266 \cdot 270 \cdot \frac{1}{1 0 ^{12}} ln (- \frac{4.5}{5} + 1)

Multiplicar fracciones:

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

= - \frac{1 \cdot ln ( 1 - \frac{4.5}{5} ) \cdot 266 \cdot 270}{1 0 ^{12}}

Multiplicar los numeros:

1 \cdot 266 \cdot 270 = 71820

= - \frac{71820 ln ( - \frac{4.5}{5} + 1 )}{1 0 ^{12}}

Cancelar

\frac{71820 ln ( 1 - \frac{4.5}{5} )}{1 0 ^{12}} : \frac{3 ^{3} \cdot 7 \cdot 19 ln ( - \frac{4.5}{5} + 1 )}{5 ^{11} \cdot 2 ^{10}}

= - \frac{3 ^{3} \cdot 7 \cdot 19 ln ( - \frac{4.5}{5} + 1 )}{5 ^{11} \cdot 2 ^{10}}

Multiplicar los numeros:

7 \cdot 19 = 133

= - \frac{3 ^{3} \cdot 133 ln ( - \frac{4.5}{5} + 1 )}{5 ^{11} \cdot 2 ^{10}}

Dividir:

\frac{4.5}{5} = 0.9

= - \frac{3 ^{3} \cdot 133 ln ( 1 - 0.9 )}{5 ^{11} \cdot 2 ^{10}}

Sumar/restar lo siguiente:

- 0.9 + 1 = 0.1

= - \frac{3 ^{3} \cdot 133 ln ( 0.1 )}{5 ^{11} \cdot 2 ^{10}}

133 \cdot 3^{3} ln (0.1) = 3591 ln (0.1)

= - \frac{3591 ln ( 0.1 )}{5 ^{11} \cdot 2 ^{10}}

5^{11} \cdot 2^{10} = 50000000000

= - \frac{3591 ln ( 0.1 )}{50000000000}

Convertir el elemento a una forma decimal

\frac{3591}{50000000000} = 7.182 E - 8

= - 7.182 E - 8 ln (0.1)

Simplificar

ln (0.1) : - 2.30258 \dots

= - (- 2.30258 \dots) \cdot 7.182 E - 8

Aplicar la regla

- (- a) = a

= 7.182 E - 8 \cdot 2.30258 \dots

Multiplicar los numeros:

7.182 E - 8 \cdot 2.30258 \dots = 1.65372 E - 7

= 1.65372 E - 7

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