Find the time required for the remaining amount to reach half its initial level. I don't understand how to to solve this step to get t = 13.1576 hrs. Could someone explain?

Find t such that A(t) = 20/2 = 10
20 * 0.9^(t/2) = 10
0.9^(t/2) = 0.5
ln(0.9^(t/2)) = ln(0.5)
t/2 ln(0.9) = ln(0.5)
t = 2 ln(0.5)/ln(0.9)
t = 13.1576 hrs

Question

Find the time required for the remaining amount to reach half its initial level. I don't understand how to to solve this step to get t = 13.1576 hrs. Could someone explain?

Find t such that A(t) = 20/2 = 10
20 * 0.9^(t/2) = 10
0.9^(t/2) = 0.5
ln(0.9^(t/2)) = ln(0.5)
t/2 ln(0.9) = ln(0.5)
t = 2 ln(0.5)/ln(0.9)
t = 13.1576 hrs

anonymous · Answer

looks good, what's the problem?

anonymous · Answer

I don't understand the step to get
t = 13.1576 hrs

anonymous · Answer

t = 2 ln(0.5)/ln(0.9)

just put it in your calculator and you get 13.1576...

anonymous · Answer

ah, okay.... thanks. is there another way to get the same answer without using LN? I'm only taking Liberal Arts Math and I don't think our teacher requires us to know how to solve problems with it

anonymous · Answer

In order to isolate the unknown exponent you have to take the log of both sides of the equation.  You can use any log though, not just the natural log ln. Just make sure you use the same base log on both sides of the equation.