Q:

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

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!  

A:

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?