Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 193: 34

$t\approx1.226$

First, take the natural log of both sides to get $$\ln \frac{2}{7}=\ln [(0.6)^{2t}]$$ Using the fact that $\ln a^b=b \ln a$, the equation simplifies to $$\ln \frac{2}{7}=2t \ln 0.6$$ Divide both sides by $2 \ln 0.6$ to get $$t=\frac{\ln \frac{2}{7}}{2\ln 0.6}=1.226$$