A mountain bike purchased for $500 goes down in value 3% each year. When is it worth $100?

If it  loses 3%  of  its value  every year, it is  worth  onl 97% of its value from the previous year.....so....

100  =  500 (.97)^N            divide  both sides  by  500

1/5  = .97^N                      take the log of both sides

log (1/5) =  log .97^N           and we can write

log (1/5) = N * log .97           divide both sides by log .97

log (1/5)  /log .97  = N ≈   52.8   ≈  53    years