The Microbit FAQ has some guidance: https://support.microbit.org/support/solutions/articles/19000129031-data-logging-faq.  They estimate ~11,000 entries of a single column of data, about 6,000 if there are two columns for each row, etc.   Based on that and a few other hints, I think the Flash memory reserved for the log is about 60 kilobytes (i.e.,could store about 60,000 individual digits).  Every row that's placed in the log will be in CSV-like format with a character separating items and rows.  (I plan to test this when time permits)

It looks like the micro:bit power consumption is often around 15mW without any lights or other I/O on (https://support.microbit.org/support/solutions/articles/19000075661-power-consumption- ).  That can be used to estimate the current draw of about 5mA (P=I*V;  0.015W = I*3v;  I=0.015W/3v = 0.005A = 5mA). 

 

AAA alkaline batteries are about 850-1200 mAH of charge (https://en.wikipedia.org/wiki/AAA_battery).  So maybe 170-240 hours at best (that's 850mAh/5mA  to 1200mAh/5mA) or 7-10 days....Realistically it's probably more like 5-7days.   AA batteries would be about twice that. Heavy screen usage probably cuts the time in half. 

A few on-line calculators:

https://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-battery-life and https://oregonembedded.com/batterycalc.htm .

I've heard complaints about connecting and disconnecting the battery pack.   The v2 can be put in sleep mode instead: https://support.microbit.org/support/solutions/articles/19000120358-how-do-i-power-off-or-put-the-micro-bit-to-sleep- 

Or, I think one of the Champions made or mentioned a tool to remove the battery connector.  I can't remember who and didn't save the link, but there are a few on thingiverse, like https://www.thingiverse.com/thing:3522758 .

Other misc: Downloads to print extra battery pack holders are at: https://microbit.org/get-started/user-guide/battery-pack-holder/ (I haven't tried it in a cutter, like a Cricut, yet).