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