# How do you calculate #log_2 10#?

##### 1 Answer

#### Answer:

#### Explanation:

It helps to write this in another way to understand what is being asked. We can write log form in exponential form

If

Which power of 2 is equal to 10? It is obviously not a whole number because the powers of 2 are: 2, 4, 8, 16 , 32 .....

So

**Using index form first,** find the log of both sides:

We know log 10 = 1, but need to use a calculator to find log2.

**Using log form,** this can be written using the change of base rule:

This is the same result as was found the first time.

Now use a calculator to find the answer as