calculate logarithm base 2 of number very close to 1

I need to calculate logarithm base 2 of number very close to 1. for example
log2(0.9999999999999999999999999999999… The expected result is around 2^-80.
I can't calculate it even with Matlab.
Anyone can help me?

0.999... - Wikipedia, the free encyclopedia...
$log_2$ 0,(9) = 0

Quote:

Originally Posted by thehealer

I need to calculate logarithm base 2 of number very close to 1. for example
log2(0.9999999999999999999999999999999… The expected result is around 2^-80.
I can't calculate it even with Matlab.
Anyone can help me?

Remembering the 'logarithmics series'...

http://quicklatex.com/cache3/ql_3f98...8392081_l3.png (1)

... setting http://quicklatex.com/cache3/ql_9807...7e7fce6_l3.png if http://quicklatex.com/cache3/ql_cd0d...ddc6b5a_l3.png is...

http://quicklatex.com/cache3/ql_d95c...edffbc3_l3.png (2)

Kind regards

$\chi$ $\sigma$

thank you