Question 850169
EDITED: No need for any Change of Base.


n hours_____________Count
0___________________6
1___________________6*2
{{{2___________________6*2*2=6*2^2}}}
3___________________{{{6*2*2*2=6*2^3}}}
.
.
.
n___________________{{{6*2^n}}}


Relation:  {{{highlight(a=6*2^n)}}}, n is the count of finished hours; a is the count of bacteria.


If a=1000000, what is n?
{{{6*2^n=1000000}}}
{{{2^n=1000000/6=166666&2/3}}}
{{{2^n=166666&2/3}}}
-
{{{log(10,2^n)=log(10, 166666&2/3)}}}
{{{n*log(10,2)=log(10, 166666&2/3)}}}

{{{n=log(10,166666&2/3)/log(10,2)}}}
{{{n=5.2218/(0.30103)}}}
{{{highlight(n=17.34)}}} hours
17 hours 21 minutes