A radioactive isotope decayed to 1732 of its original mass after 60 minutes. Find the half-life of this radioisotope.
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You typed '1732' where you may have meant 1/732 or 17/32. Let's use 17/32.
17/32 = 0.53125 (this is the decimal amount that remains)
(1/2)^n = 0.53125
n log 0.5 = log 0.53125
n = 0.91254 (this is how many half-lives have elapsed)
60 min divided by 0.91254 = 65.75 min (this is the half-life, which you may round off to 66 min, if you so desire)
17/32 = 0.53125 (this is the decimal amount that remains)
(1/2)^n = 0.53125
n log 0.5 = log 0.53125
n = 0.91254 (this is how many half-lives have elapsed)
60 min divided by 0.91254 = 65.75 min (this is the half-life, which you may round off to 66 min, if you so desire)