Did you know that archaeologists use logarithms in their everyday work? I didn't. They use logarithms to determine the age of artifacts like bones or different kinds of fibers that can be up to 50,000 years old. Archaeologists use logs to compare the decaying Carbon-14 to Carbon-12.
x=(1/2)^t/5730
where x is the proportion of Carbon-14 remaining in the object after t years.
Example: x=(1/2)^(64/5730) x=.9923
t= age(x) = 5730ln(x)/ln(1/2)
where x is the proportion of Carbon-14 remaining in the object after t years and t is the age of the object.
Example: 5730ln(.9923)/ln(1/2) t=64
x=(1/2)^t/5730
where x is the proportion of Carbon-14 remaining in the object after t years.
Example: x=(1/2)^(64/5730) x=.9923
t= age(x) = 5730ln(x)/ln(1/2)
where x is the proportion of Carbon-14 remaining in the object after t years and t is the age of the object.
Example: 5730ln(.9923)/ln(1/2) t=64