Question

How do you evalute `Log_ 3 (18)`?

Answer 1

`log_3(18)=2+log_3(2)approx2.6309`

Explanation:

`log_3(18)=log_3(3^2xx2)`

Use the rule: `log_a(bc)=log_a(b)+log_a(c)`

`=>log_3(3^2)+log_3(2)`

Use the rule: `log_a(a^b)=b`

`=>2+log_3(2)`

This is a simplified answer. However, if you want your answer in decimal form, use a calculator. Since many calculators don't have the capability of finding logarithms with a specific base, use the change of base formula.

`log_a(b)=(log_c(b))/(log_c(a))`

Thus, since the `ln` button is on most calculators (or just the `log` button),

`log_3(2)=ln(2)/ln(3)=log(2)/log(3)approx0.6309`

Thus,

`log_3(18)=2+log_3(2)approx2.6309`