Question 877637
What you should already know:


{{{100(1.02)^(2t)=50000}}}

{{{(100/100)1.02^(2t)=50000/100}}}

{{{1.02^(2t)=500}}}



What you are studying how to do now:

{{{log((1.02^(2t)))=log((500))}}}
{{{2t*log((1.02))=log((5*10^2))}}}
{{{2t*log((1.02))=2*log((5*10))}}}
{{{t*log((1.02))=log((5*10))}}}
{{{t=log((5*10))/log((1.02))}}}

How to continue this depends on what base you want.  Base ten might be most convenient.


{{{t=(log(10,5*10))/(log(10,1.02))}}}


{{{t=(log(10,5)+log(10,10))/(log(10,1.02))}}}


{{{highlight(t=((log(10,5))+1)/log(10,1.02))}}}