\(\begin{array}{ll} 4000=2000\left(1+\frac{0.06}{12}\right)^{N \times 12} & \text{Divide both sides by 2000} \\ 2=(1.005)^{12 N} & \text{To solve for the exponent, take the log of both sides} \\ \log ...4000=2000(1+0.0612)N×12Divide both sides by 20002=(1.005)12NTo solve for the exponent, take the log of both sideslog(2)=log((1.005)12N)Use the exponent property of logs on the right sidelog(2)=12Nlog(1.005)Now we can divide both sides by 12log1.005log(2)12log(1.005)=NApproximating this to a decimalN=11.581
