Question

convierte cada expresion en un unico logaritmo

Answer 1

Para resolverlo simplemente deberemos aplicar propiedades logarítmicas.

a) 3$log_{5}$a + 4$log_{5}$b

Aplicando la propiedad de logaritmo de una potencia:

$log_{5}$a³ + $log_{5}$b⁴

= $log_{5}$(a³ × b⁴)

b) 0.5$log_{0.5}$a - 3$log_{0.5}$a

=$log_{0.5}a^{0.5}$ - $log_{0.5}a^{3}$

= $log_{0.5}(a^{0.5}/a^{3} )$

= $log_{0.5}(1/a^{-5/2} )$

c) 2($log_{4} x$+2$log_{4}y$-3$log_{3}z$)

= 2($log_{4} x$+$log_{4}y^{2}$-$log_{3}z^{3}$)

= 2($log_{4}(x*y^{2})$-$log_{3}z^{3}$)

Answer 2

Respuesta:

) 3log_{5}a + 4log_{5}b

log_{5}a³ + log_{5}b⁴

= log_{5}(a³ × b⁴)

b) 0.5log_{0.5}a - 3log_{0.5}a

=log_{0.5}a^{0.5}  - log_{0.5}a^{3}  

= log_{0.5}(a^{0.5}/a^{3} )  

= log_{0.5}(1/a^{-5/2} )  

c) 2(log_{4} x+2log_{4}y-3log_{3}z)

= 2(log_{4} x+log_{4}y^{2}-log_{3}z^{3})

= 2(log_{4}(x*y^{2})-log_{3}z^{3})