Question

How do I write log3 5 using natural logarithms?

Answer 1

Answer:

$\log_3 5=\frac{\ln(5)}{\ln(3)}$

Step-by-step explanation:

We want to write:

$\log_3 5$

Using natural logarithms.

We can use the following property of logarithms (the change of base):

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

Hence, if we let c be equal to the natural number e:

$\log_b a=\frac{\ln(a)}{\ln(b)}$

So, we will substitute 5 for a and 3 for b. This yields:

$\log_3 5=\frac{\ln(5)}{\ln(3)}$

And we are finished.