Im trying to figure out half life?

Question

the given equation is 10=.1e^(.26t)

t represents time. how do i find t?

Answer 1

ln(10)=ln{.1e^(.26t)}

ln(10) = .1*.26t

t = ln(10)/.1*.26

Answer 2

You want to solve this equation for t.

First divide both sides by .1 to get

100 = e^(.26t)

Now take the natural log of both sides

ln 100 = ln e^(.26t)

This equals

ln 100 = .26t   (since ln e = 1)

Now divide by .26

ln 100 / .26 = t

t = 17.71219    or   about 17.7

Have a good day!

EDIT:  I'm sorry but Barca (above) is wrong! You cannot "nest" a natural log. You must first divide the value in front of e, or in this case .1, and then take the natural log of both sides.