# How do you calculate #log_10 (7)#?

##### 1 Answer

#### Answer:

You can use Newton's method to find approximations...

#### Explanation:

Here's one way to find numerical approximations for it without the benefit of a

**Newton's method**

Define

Then

Starting with approximation

#a_(i+1) = a_i - (f(a_i))/(f'(a_i)) = a_i - (10^(a_i) - 7)/(10^(a_i)*ln(10))#

Of course this requires that you are able to calculate

For example, if we use

#1.00000000000000#

#0.86971249891427#

#0.84578273695874#

#0.84509858389730#

#0.84509804001812#

#0.84509804001426#

#0.84509804001426#

Note that we do not need to know