Question 27166
Your equation is
{{{f(t) = 10^t}}}
You want to know when f(t) = 5 billion
or
{{{f(t) = 5*10^9}}} in scientific notation
so
{{{5*10^9 = 10^t}}}
Take the log of both sides
{{{log(5*10^9) = log(10^t)}}}
use the rules
log(a*b*c* ... ) = log(a) + log(b) + log(c) + ...
and 
log(10^k) = k
{{{log(5*10^9) = log(10^t)}}}
{{{log(5) + log(10^9) = log(10^t)}}}
{{{log(5) + 9 = t}}}