How do you calculate #log_2 (9)#?

1 Answer
reudhreghs
Apr 9, 2016

Enter it into a calculator. It's about #3.17#.

Explanation:

You can change it around a bit, knowing that #9 = 3^2#, so

#log_2 9 = log_2 3^2 = 2log_2 3#, but this is a longer way to get to the same answer, and you still have to use a calculator, because you can't do #2^3.17# in your head, unless you have a heavy dosage of savant syndrome.

Have decimals in exponents doesn't seem correct. It actually makes more sense as a fraction,

#2^3.17 = 2^(317/100)#

which you can then turn into a root,

#2^(317/100) = root(100)2^317#

which is actually what is meant by #2^3.17#.

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