SOLUTION: what is log2 (.008)

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Question 643945: what is log2 (.008)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C++%28.008%29%29
You should first try to figure out what this is by hand because by hand you might be able to get an exact answer. If you use a calculator you are most likely to get a decimal approximation.

This log represents the exponent for 2 that results in 0.008. Which exponent this is is not obvious. Perhaps it might help to see 0.008 in fraction form:
log%282%2C++%288%2F1000%29%29
But still the power of 2 that results in 8/1000 is not clear. So we will need to resort to our calculator.

Your calculator probably does not have a button for base 2 logs. So to find the base 2 log above we will use the base conversion formula:
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
to convert the base 2 log into an expression of logs your calculator "knows":
log%282%2C+%280.008%29%29+=+log%28%280.008%29%29%2Flog%28%282%29%29
or
log%282%2C+%280.008%29%29+=+ln%280.008%29%2Fln%282%29
Both will work and both will give the same answer.