Asked by Matthew

I asked the following the other day and received the following answer:
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
Answered by Matthew
nevermind on 2), i would appreciate an asnwer to 1) though
Answered by Reiny
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
<b>LOG</b> .5^(10/k) = <b>LOG</b> .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
Answered by Matthew
but why the choice for ln?
There are no AI answers yet. The ability to request AI answers is coming soon!