Question

$log5 \div 2 =$
how can i find decimal value ​

Answer 1

Explanation:

How do I approximate the logarithm to four decimal places using the change of base formula: log5 1/2?

Ok, the log5 1/2.

The change of base formula here is log(1/2)/log(5), where 'log' is a logarithm in any base (as long as we use the same base for both logs).

Let's take base 10. In order to calculate this we will only need log 2. A lot of people have this number memorized: 0.30103.

Even if you don't have the number memorized, here is how to make a good estimate: 2^10 = 1024. log(1024) is a tiny bit more than 3, so log(2) needs to be a tiny bit more than 0.3.

if log(2) is 0.3, then log(1/2) = -0.3 and log(5) = 1-0.3 = 0.7.

The answer therefore is -0.3/0.7 = -0.428....

Use 0.30103 instead of 0.3 will give you an answer to 4 decimal places correct.

I leave it up to you to do this.