Algebra involving powers of two when solving for cardinality involving power sets What's the proper

prensistath

prensistath

Answered question

2022-05-21

Algebra involving powers of two when solving for cardinality involving power sets
What's the proper way of solving this problem (self study)?
Find m if | A | = m, | B | = m + 2 and | P ( B ) | | P ( A ) | = 48
Since the numbers are small, I can get m=4 pretty much by inspection
I tried the more general approach of making the equation and solving for m, but got stuck because my algebra skills are weak:
2 ( m + 2 ) 2 m = 48
However, l o g 2 ( 48 ) is hanging me up. Plugging in m = 4 does satisfy the equation, so I'm just messing up something really obvious here.

Answer & Explanation

Meadow Knox

Meadow Knox

Beginner2022-05-22Added 12 answers

You are applying log 2 at an unnatural position (for, log 2 of a difference doesn't simplify nicely).
2 m + 2 2 m = 4 2 m 2 m = 3 2 m
Now we get:
3 2 m = 48 2 m = 16
At this point, using log 2 is fruitful.

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