A sample initially contains only U-238 isotope of uranium. With...

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into $\mathrm{Pb}-206$ while the rest of it remains undisintegrated. When the age of the sample is $\mathbf{P} \times 10^8$ years, the ratio of mass of $\mathrm{Pb}-206$ to that of $\mathrm{U}-238$ in the sample is found to be 7 . The value of $\mathbf{P}$ is ______ [Given: Half-life of U-238 is $4.5 \times 10^9$ years; $\log _c 2=0.693$ ]