Now, I need to prove OR disprove that f(n) = O(g(n)) implies 2^(f(n)) = O(2^g(n))). Intuitively, this makes sense, so I figured I could prove it with help from the previous theorem. I noticed that f(n) can be rewritten as lg(2^f(n)) and that g(n) is just lg(2^g(n)) , which got me excitedthis is taking the log base 2 of both sides of what I want to prove, and it simplifies things a lot!

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The Swedish alphabet (Swedish: Svenska alfabetet) is a basic element of the Latin writing system used for the Swedish language. The 29 letters of this alphabet are the modern 26-letter basic Latin alphabet (A through Z) plus Å, Ä, and Ö, in that order. It contains 20 consonants and 9 vowels (a e i o u y å ä ö). g, /ɡ/, /j/, /j/ before front vowels ⟨e i y ä ö⟩, otherwise /ɡ/.

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