[summary: $~$\log_2(3) \approx 1.585.$~$ This can be interpreted a few different ways:

- If you multiply the number of messages you might want to send by 3, then the cost of encoding the message will go up by 1.58 bits on average.
- If you pack $~$n$~$ of independent and equally likely 3-messages together into one giant $~$3^n$~$ message, then the cost (in bits) per individual 3-message drops as $~$n$~$ grows, ultimately converging to $~$\log_2(3)$~$ bits per 3-message as $~$n$~$ gets very large.
- The infinite expansion of $~$\log_2(3) = 1.58496250072\ldots$~$ tells us not just how many bits it takes to send one 3-message $~$(\approx \lceil 1.585 \rceil = 2)$~$ but also how long it takes to send any number of 3-messages put together. For example, it costs 2 bits to send one 3-message; 16 bits to send 10; 159 bits to send 1000; 1585 to send 10,000; 15850 to send 100,000; 158497 to send 1,000,000; and so on. ]

There are [3nd $~$\log_2(3) \approx 1.585$~$] bits to a Trit. This can be interpreted a few different ways:

- If you multiply the number of messages you might want to send by 3, then the cost of encoding the message will go up by 1.58 bits on average. See [+marginal_message_cost] for more on this interpretation.
- If you pack $~$n$~$ of independent and equally likely 3-messages together into one giant $~$3^n$~$ message, then the cost (in bits) per individual 3-message drops as $~$n$~$ grows, ultimately converging to $~$\log_2(3)$~$ bits per 3-message as $~$n$~$ gets very large. For more on this, see [+average_message_cost] and the GalCom example of encoding trits using bits.
- The infinite expansion of $~$\log_2(3) = 1.58496250072\ldots$~$ tells us not just how many bits it takes to send one 3-message $~$(\approx \lceil 1.585 \rceil = 2)$~$ but also how long it takes to send any number of 3-messages put together. For example, it costs 2 bits to send one 3-message; 16 bits to send 10; 159 bits to send 1000; 1585 to send 10,000; 15850 to send 100,000; 158497 to send 1,000,000; and so on. For more on this interpretation, see the [log_series_of_ceilings "series of ceilings"] interpretation of logarithms.