simplificar 1/(-(0.005))[0.8ln(1/8)+0.2ln(9/2)]

Solución

simplificar

\frac{1}{- ( 0.005 )} [0.8 ln (\frac{1}{8}) + 0.2 ln (\frac{9}{2})]

- \frac{1}{0.005} ln (0.25595 \dots)

Notación decimal

272.54755 \dots

Pasos de solución

\frac{1}{- ( 0.005 )} [0.8 ln (\frac{1}{8}) + 0.2 ln (\frac{9}{2})]

Aplicar las propiedades de los logaritmos:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.8 ln (\frac{1}{8}) = ln ((\frac{1}{8})^{0.8})

= \frac{1}{- ( 0.005 )} [0.2 ln (\frac{9}{2}) + ln ((\frac{1}{8})^{0.8})]

Aplicar las propiedades de los logaritmos:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.2 ln (\frac{9}{2}) = ln ((\frac{9}{2})^{0.2})

= \frac{1}{- ( 0.005 )} [ln ((\frac{1}{8})^{0.8}) + ln ((\frac{9}{2})^{0.2})]

Aplicar las propiedades de los logaritmos:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((\frac{1}{8})^{0.8}) + ln ((\frac{9}{2})^{0.2}) = ln ((\frac{1}{8})^{0.8} (\frac{9}{2})^{0.2})

= \frac{1}{- 0.005} [ln ((\frac{1}{8})^{0.8} (\frac{9}{2})^{0.2})]

(\frac{1}{8})^{0.8} (\frac{9}{2})^{0.2} = 0.25595 \dots

= \frac{1}{- 0.005} [ln (0.25595 \dots)]

Quitar los parentesis:

(a) = a

= \frac{1}{- 0.005} ln (0.25595 \dots)

Aplicar las propiedades de las fracciones:

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

= - \frac{1}{0.005} ln (0.25595 \dots)

ln (e^{x} sin (2 x))

\frac{ln ( \frac{A}{b} )}{2 ln ( 10 )}

\frac{1}{2} ln (2 x + 5) - \frac{1}{3} ln (x + 8) + ln (C)

- lo g_{10} (7.83 \cdot 1 0^{- 8})

ln (8 \cdot 12)