How do you calculate #log_2 10#?

1 Answer
EZ as pi
Jun 8, 2016

#x = 3.3219#

Explanation:

It helps to write this in another way to understand what is being asked. We can write log form in exponential form
If #log_2 10 = x " " rArr 2^ x = 10#

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 #x# lies between 3 and 4.

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

#log 2^x = log 10 " " rArr xlog2 = log10#
#" " x = log10/log2#

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:

#log_2 10 = x " " x = log10/log2#
This is the same result as was found the first time.

Now use a calculator to find the answer as #x = 3.3219# which is exactly as we expected, somewhere between 3 and 4.

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