King's Challenge:Hartely's Formula

a$)$ There are ten coins on the table, identical in appearance. Nine of them are pure gold and one is false, differing from others by weight $($it could be heavier or lighter than the pure$).$ Also on the table is a simple balance scale. Device a scheme whereby the false coin can be identified without fail through only three weighing's with the scale.

Given Hartley$$s Formula I $=$ R Log$2(1/$p$)$ and that

Log$2(10)=3\mathrm{.}32$ bits

Log$2(8)=3\mathrm{.}0$ bits

Log$2(5)=2\mathrm{.}32$ bits

Log$2(4)=2\mathrm{.}0$ bits

Log$2(3)=1\mathrm{.}58$ bits

Log$2(2)=1\mathrm{.}0$ bits

Log$2(1)=0\mathrm{.}0$ bits

What is the amount of information needed to identify the False Coin with certainty?