I asked the following the other day and received the following answer:

Question

Posted by Matthew on Sunday, March 17, 2013 at 11:03pm.

A quantity of oxygen gas had 16.32 g of the radioactive isotope oxygen-19 in it. When measured exactly 10 minutes later, the amount of oxygen-19 was 0.964 g. What is the half-life, in seconds, of oxygen-19?

math - Reiny, Monday, March 18, 2013 at 12:05am

16.32(1/2)^(t/k) = .964 , where t is in minutes, and k is the half-life in minutes.
(.5)^(10/k) = .0590686.. ( I stored it)
ln both sides

(10/k) ln .5= ln (.059068...)
10/k = 4.081464...
k = 2.4504 minutes or 147.006 seconds

I would like to know
1) How does this mathematically work, how can i ln both sides suddenly?
2) Secondly, how does the last answer occur- like this part is not giving me the same outcome:
10/k = 4.081464...
k = 2.4504 minutes or 147.006 seconds

Answer 1

nevermind on 2), i would appreciate an asnwer to 1) though

Answer 2

log( ? ) is a mathematical operation, just like taking a square root, cubing something of finding the sine of something

Basic rules of an equation: Whatever you do to one side, you must do to the other side.

so if I have
.5^(10/k) = .059..

my doing
LOG .5^(10/k) = LOG .059...
I am doing just that, whatever I did to the left side, I did to the right side.

If you don't know logarithms (logs), then there is no way you can solve this equation, other than plain old trial and error guessing

Answer 3

but why the choice for ln?