Artificial intelligent assistant

Half life of a radioactive sample > The half of thallium-$201$ is $73$ hrs. How many hours will it take for an amount of thallium-$201$ to decay so that only $5%$ of the original amount remains ? So I decide to use this $$0.05P=P(0.05)^{73}$$ Got confused

A half life of $73$ hours means that after $t$ hours, what remains is $$ 0.5^{t/73} $$ of the original substance. (Note how, for $t=73$, the exponent becomes $1$, so we are left with $0.5$ of the original substance, exactly like we are supposed to. This is a quick check to make sure we have the right expression.)

Now you want to find the value of $t$ for which $5\%$ of the original substance is left. That means that you want to solve $$ 0.05=0.5^{t/73} $$

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