A=P(1+r)^n
A=10000(1.06)^n
2=10000(1.06)^n
log(2)=log(1.06)^n (take the log of both sides of an eqn)
n=log2/log(1.06) (divide both sides of the equation)
n=11.895..
n=12 years
Remember
One of the properties of logarithmic equations is that log(a^b) = b*log(a).