Answer:
[tex]\log_{11}(5)=0.671[/tex] and [tex]\log_4(40)=2.661[/tex]
Step-by-step explanation:
Given: [tex]\log_{11}5[/tex] and [tex]\log_{4}40[/tex]
We have to rewrite each logarithm as a quotient of natural logarithms.
Using property of logarithm,
[tex]\log_a(b)=\frac{\log_eb}{\log_ea}[/tex]
Consider 1) [tex]\log_{11}5[/tex]
Applying property stated above,
[tex]\log_{11}(5)=\frac{\log_e5}{\log_e11}[/tex]
We have [tex]{\log_e5}=1.609[/tex](approx)
[tex]{\log_e11}=2.398[/tex](approx)
Substitute, we get,
[tex]\log_{11}(5)=0.671[/tex]
Consider 2) [tex]\log_{4}40[/tex]
Applying property stated above,
[tex]\log_4(40)=\frac{\log_e40}{\log_e4}[/tex]
We have [tex]{\log_e40}=3.689[/tex](approx)
[tex]{\log_e4}=1.386[/tex](approx)
Substitute, we get,
[tex]\log_4(40)=2.661[/tex]
Thus, [tex]\log_{11}(5)=0.671[/tex] and [tex]\log_4(40)=2.661[/tex]
