# How do you solve #log_10 2#?

##### 1 Answer

#### Answer:

#### Explanation:

One somewhat cumbersome way of calculating

First note that

If we raise

Let's see what happens:

#2^10 = 1024 >= 1000 = 10^3#

So the first digit after the decimal point is

Divide

To find the next digit of the logarithm, calculate

#1.024^10 ~~ 1.26765060022822940149#

This is still less than

Then:

#1.26765060022822940149^10 ~~ 10.71508607186267320891 >= 10^1#

So the next digit of the logarithm is

Divide

Then:

#1.071508607186267320891^10 ~~ 1.99506311688075838379#

This is still less than

Then:

#1.99506311688075838379^10 ~~ 999.00209301438450246726#

That is very close to

Putting our digits together