Question 137588
The problem is in your base. 
You are not using base 10.
Here's the equation that describes your problem.
{{{N(t)=N[0](1.05)^t}}}
At time t=0, your population is {{{N[0]}}}.
You're looking for t when {{{N(t)=2*N[0]}}}
{{{2*N[0]=N[0](1.05)^t}}}
{{{2=(1.05)^t}}}
The base for your logarithm is 1.05. 
{{{log(1.05,2)=t}}}
You can transform that into a base 10 problem with a substitution.
{{{t=log(10,2)/log(10,1.05)}}}
{{{t=0.30103/.021189)}}}
{{{t=14.2067)}}}
The time to double is 14.2067 years. 
Checking the answer, you get:
{{{N(t)=2N[0]}}}