If we start with Q milligrams of radium, the amount (q) remaining after T years is given by q=Q(2)^(-T/1600). Express T in terms of q and Q?

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Answer 1 · 2018-05-15T16:29:15

#T=1600/log2log(Q/q)#

#q=Qxx2^(-1/1600T)#

Take logs of both sides, where #log# means log to any base.

#logq=log(Qxx2^(-1/1600T))#

Using the multiplication law

#logq=logQ+log(2^(-1/1600T))#

Using the powers law

#logq=logQ-1/1600Tlog2#

#logQ-logq=1/1600Tlog2#

#T=1600/log2(logQ-logq)#

#T=1600/log2log(Q/q)#