Respuesta :
Answer:
(a)[tex]\log_3(\dfrac{81}{3})=3[/tex]
(b)[tex]\log_5(\dfrac{625}{25})=2[/tex]
(c)[tex]\log_2(\dfrac{64}{8})=3[/tex]
(d)[tex]\log_4(\dfrac{64}{16})=1[/tex]
(e)[tex]\log_6(36^4)=8[/tex]
(f)[tex]\log(100^3)=6[/tex]
Step-by-step explanation:
Let as consider the given equations are [tex]\log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?[/tex].
(a)
[tex]\log_3(\dfrac{81}{3})=\log_3(27)[/tex]
[tex]\log_3(\dfrac{81}{3})=\log_3(3^3)[/tex]
[tex]\log_3(\dfrac{81}{3})=3[/tex] [tex][\because \log_aa^x=x][/tex]
(b)
[tex]\log_5(\dfrac{625}{25})=\log_5(25)[/tex]
[tex]\log_5(\dfrac{625}{25})=\log_5(5^2)[/tex]
[tex]\log_5(\dfrac{625}{25})=2[/tex] [tex][\because \log_aa^x=x][/tex]
(c)
[tex]\log_2(\dfrac{64}{8})=\log_2(8)[/tex]
[tex]\log_2(\dfrac{64}{8})=\log_2(2^3)[/tex]
[tex]\log_2(\dfrac{64}{8})=3[/tex] [tex][\because \log_aa^x=x][/tex]
(d)
[tex]\log_4(\dfrac{64}{16})=\log_4(4)[/tex]
[tex]\log_4(\dfrac{64}{16})=1[/tex] [tex][\because \log_aa^x=x][/tex]
(e)
[tex]\log_6(36^4)=\log_6((6^2)^4)[/tex]
[tex]\log_6(36^4)=\log_6(6^8)[/tex]
[tex]\log_6(36^4)=8[/tex] [tex][\because \log_aa^x=x][/tex]
(f)
[tex]\log(100^3)=\log((10^2)^3)[/tex]
[tex]\log(100^3)=\log(10^6)[/tex]
[tex]\log(100^3)=6[/tex] [tex][\because \log10^x=x][/tex]
