Question

How do I write log3 5 using natural logarithms?

Answer 1

Answer:

$\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}$

Step-by-step explanation:

We want to write:

$\log_3 5$

Using natural logarithms.

We can use the following property of logarithms:

$\displaystyle \log_b a=\frac{\log_c a}{\log_c b}$

Hence, if we let c be equal to e:

$\displaystyle \log_b a= \frac{\log _e a}{\log _e b} = \frac{\ln a}{\ln b}$

Then by letting a = 5 and b = 3:

$\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}$