<prompt> Tathmini frac 2log_420006 frac 3log_520006,ukitoa jibu lako kama sehemu katika maneno ya chini kabisa.  <response>: Kwa kutumia sifa log_a bx x log_a b, tuna beginaligned frac 2log_420006 frac 3log_520006 frac26log_4 2000 frac36log_5 2000 frac13log_4 2000 frac12log_5 2000. endalignedKwa kuwa log_a b frac1log_b a, basi tunaweza kuandika frac13log_4 2000 frac12log_5 2000 frac13log_2000 4 frac12log_2000 5,ambayo ni sawa na log_2000 413 512 logi_2000 223 512.Tangu 2000 24 53 kushoto2 23 512kulia6, usemi tfrac16. 