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simplificar 2610^{-3}ln((10^{18})/(1*10^{10)})

Solución

simplificar

26 \cdot 1 0^{- 3} \cdot ln (\frac{1 0 ^{18}}{1 \cdot 1 0 ^{10}})

Solución

\frac{26 ln ( 10 )}{125}

+1

Notación decimal

0.47893 \dots

Pasos de solución

26 \cdot 1 0^{- 3} ln (\frac{1 0 ^{18}}{1 \cdot 1 0 ^{10}})

Aplicar las leyes de los exponentes:

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

= 26 \cdot \frac{1}{1 0 ^{3}} ln (\frac{1 0 ^{18}}{1 0 ^{10} \cdot 1})

Multiplicar fracciones:

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

= \frac{1 \cdot 26 ln ( \frac{1 0 ^{18}}{1 \cdot 1 0 ^{10}} )}{1 0 ^{3}}

1 \cdot 26 ln (\frac{1 0 ^{18}}{1 \cdot 1 0 ^{10}}) = 26 ln (\frac{1 0 ^{18}}{1 0 ^{10}})

= \frac{26 ln ( \frac{1 0 ^{18}}{1 0 ^{10}} )}{1 0 ^{3}}

Factorizar

26 : 2 \cdot 13

Factorizar

1 0^{3} : 2^{3} \cdot 5^{3}

= \frac{2 \cdot 13 ln ( \frac{1 0 ^{18}}{1 0 ^{10}} )}{2 ^{3} \cdot 5 ^{3}}

Eliminar los terminos comunes:

2

= \frac{13 ln ( \frac{1 0 ^{18}}{1 0 ^{10}} )}{5 ^{3} \cdot 2 ^{2}}

\frac{1 0 ^{18}}{1 0 ^{10}} = 1 0^{8}

= \frac{13 ln ( 1 0 ^{8} )}{5 ^{3} \cdot 2 ^{2}}

Simplificar

ln (1 0^{8}) : 8 ln (10)

= \frac{13 \cdot 8 ln ( 10 )}{5 ^{3} \cdot 2 ^{2}}

Multiplicar los numeros:

13 \cdot 8 = 104

= \frac{104 ln ( 10 )}{5 ^{3} \cdot 2 ^{2}}

Factorizar

104 : 2^{3} \cdot 13

= \frac{2 ^{3} \cdot 13 ln ( 10 )}{5 ^{3} \cdot 2 ^{2}}

Cancelar

\frac{2 ^{3} \cdot 13 ln ( 10 )}{5 ^{3} \cdot 2 ^{2}} : \frac{2 \cdot 13 ln ( 10 )}{5 ^{3}}

= \frac{2 \cdot 13 ln ( 10 )}{5 ^{3}}

Multiplicar los numeros:

2 \cdot 13 = 26

= \frac{26 ln ( 10 )}{5 ^{3}}

5^{3} = 125

= \frac{26 ln ( 10 )}{125}

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