# Is the logarithm function injective (one-to-one)?

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

To put it simply, does $\log_2(x) = \log_2(y) \implies x = y$?

I.e., as $x$ and also $y$ remain in the very same log base, can I simply go down the logs?

Many thanks!

2
2022-06-07 14:33:09
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What does it suggest for a number $a$ to be equivalent to $\log_2(x)$? It suggests that $2^a=x$.