Is 1+lgi=lg(i+i)? I've been studying Sedgewick's "Algorithms" book and in proof of one proposition he writes the following: the property is preserved because 1+lg i=lg(i+i)<=lg(i+j)=lg k

nyle2k8431 2022-11-20 Answered
Is 1 + lg i = lg ( i + i )?
I've been studying Sedgewick's "Algorithms" book and in proof of one proposition he writes the following:
the property is preserved because
1 + lg i = lg ( i + i ) lg ( i + j ) = lg k
I cannot wrap my brain around the first part of this inequation, namely 1 + lg i = lg ( i + i ). Can anyone offer an explanation? Thanks in advance!
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Answers (1)

Biardiask3zd
Answered 2022-11-21 Author has 16 answers
The l g function is the logarithm to the base 2 (or binary logarithm), that is, l g 2 = 1. Thus
l g ( i + i ) = l g ( 2 i ) = l g 2 + l g i = 1 + l g i
By the way, the l g function can also be defined by l g ( x ) = log x log 2 .
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