1. **State the problem:** Solve the equation $$201 \cdot 2^x = 67$$ for $x$. 2. **Isolate the exponential term:** Divide both sides by 201 to get $$2^x = \frac{67}{201}$$. 3. **Show the cancellation step:** $$2^x = \frac{\cancel{67}}{\cancel{201}}$$ (no common factors to cancel here, so fraction remains as is). 4. **Take the logarithm of both sides:** Use the natural logarithm (ln) to get $$\ln(2^x) = \ln\left(\frac{67}{201}\right)$$. 5. **Use the logarithm power rule:** $$x \ln(2) = \ln\left(\frac{67}{201}\right)$$. 6. **Solve for $x$:** $$x = \frac{\ln\left(\frac{67}{201}\right)}{\ln(2)}$$. 7. **Calculate the numerical value:** $$x \approx \frac{\ln(0.3333)}{\ln(2)} \approx \frac{-1.0986}{0.6931} \approx -1.5849$$. **Final answer:** $$x \approx -1.585$$.