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Is the logarithm function injective (or, one-to-one)?

In other words, does $\log_2(x) = \log_2(y) \implies x = y$?

I.e., as $x$ and $y$ are in the same log base, can I just drop the logs?

Thanks!

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    You asked a [question](http://math.stackexchange.com/questions/23704/does-log-b-left-x-right-log-b-left-y-right-rightarrow-x-y) of which this is clearly a special case in February. Is there something that wasn't cleared up by the answers there?2011-05-22

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What does it mean for a number $a$ to be equal to $\log_2(x)$? It means that $2^a=x$.

Can you use this to answer the question?

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    More like $a=b$ and thus $2^a=2^b$.2011-05-22