# How do you solve #log_10 200!#?

##### 2 Answers

Let

Then by definition,

Now take the log on both sides and simplify using laws of logs to get

#### Answer:

Use a computer package...

#### Explanation:

You can either ask a computer to evaluate

#log_10 (200!) = sum_(n=1)^200 log_10(n)#

Either way you have a large number of calculations to be done. The only advantage I can see of summing the logs of each number is that you will not have to deal with numbers larger than

Here are some computer generated figures:

and