How do you calculate $log_2 (3.16)$ ?

Question

2619 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T22:32:38

$log_2(3.16) = log(3.16)/log(2) ~~ 1.66$

Using the change of base formula, we have:

$log_2(3.16) = log(3.16)/log(2)$

One way of finding an approximation for this is to note that:

$sqrt(10) ~~ 3.16227766 ~~ 3.16$

So:

$log(3.16) ~~ log(10^(1/2)) = 1/2$

Also use:

$log(2) ~~ 0.30103$

Then:

$log_2(3.16) = log(3.16)/log(2) ~~ 1/(2*0.30103) = 1/0.60206 ~~ 1.66$

How do you calculate log_2 (3.16)log_2 (3.16)?