simplificar ln(1/(2pi(x^2)^{n/2)})

Solución

simplificar

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}})

- \frac{n ln ( x ^{2} )}{2} - ln (2) - ln (π)

Pasos de solución

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}})

Aplicar las propiedades de los logaritmos:

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

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}}) = ln (1) - ln (2 π (x^{2})^{\frac{n}{2}})

= ln (1) - ln (2 π (x^{2})^{\frac{n}{2}})

Aplicar las propiedades de los logaritmos:

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

ln (2 π (x^{2})^{\frac{n}{2}}) = ln (2) + ln (π) + ln ((x^{2})^{\frac{n}{2}})

= ln (1) - (ln ((x^{2})^{\frac{n}{2}}) + ln (2) + ln (π))

Aplicar las propiedades de los logaritmos:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x^{2})^{\frac{n}{2}}) = \frac{n}{2} ln (x^{2})

= ln (1) - (ln (2) + ln (π) + \frac{n}{2} ln (x^{2}))

Aplicar las propiedades de los logaritmos:

lo g_{a} (1) = 0

= 0 - (\frac{n}{2} ln (x^{2}) + ln (2) + ln (π))

Multiplicar

\frac{n}{2} ln (x^{2}) : \frac{n ln ( x ^{2} )}{2}

= 0 - (\frac{n ln ( x ^{2} )}{2} + ln (2) + ln (π))

0 - (ln (2) + ln (π) + \frac{n ln ( x ^{2} )}{2}) = - (ln (2) + ln (π) + \frac{n ln ( x ^{2} )}{2})

= - (\frac{n ln ( x ^{2} )}{2} + ln (2) + ln (π))

Poner los parentesis

= - (\frac{n ln ( x ^{2} )}{2}) - (ln (2)) - (ln (π))

Aplicar las reglas de los signos

+ (- a) = - a

= - \frac{n ln ( x ^{2} )}{2} - ln (2) - ln (π)

lo g_{b} (\frac{57}{74})

- ln (6) + ln (3)

ln (\frac{2950000 + 2200000}{2950000}) \cdot 2550

10 lo g_{10} (\frac{( 158 \cdot 1 0 ^{- 9} )}{20 \cdot 1 0 ^{- 3}})

lo g_{10} (3 - x) + lo g_{10} (4 - x^{2})