Answer:
[tex]\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}[/tex]
Step-by-step explanation:
We want to write:
[tex]\log_3 5[/tex]
Using natural logarithms.
We can use the following property of logarithms:
[tex]\displaystyle \log_b a=\frac{\log_c a}{\log_c b}[/tex]
Hence, if we let c be equal to e:
[tex]\displaystyle \log_b a= \frac{\log _e a}{\log _e b} = \frac{\ln a}{\ln b}[/tex]
Then by letting a = 5 and b = 3:
[tex]\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}[/tex]
