The ratio of (C 14)/(C 12) in a piece of wood is (1)/(8) part that...

Given half life of $C 14 = 5730$ years.

$\lambda t = ln\dfrac{{\left(C 14 / C 12\right)}_{\text{atmosphere}}}{{\left(C 14 / C 12\right)}_{\text{wood sample}}}$

As per the question,

$\dfrac{{\left(C 14 / C 12\right)}_{wood}}{{\left(C 14 / C 12\right)}_{atmosphere}} = \dfrac{1}{8}$

So, $\lambda t = \ln 8$

$\dfrac{\ln 2}{{t}_{1/2}}t = \ln 8$

$t = 3 \times {t}_{1/2} = 3 \times 5730 = 17190\text{years}$