1. **State the problem:** Solve for $x$ in the equation $7.19 = 6.1 + \log\left(\frac{6}{0.03x}\right)$. 2. **Isolate the logarithm:** Subtract 6.1 from both sides to get $$7.19 - 6.1 = \log\left(\frac{6}{0.03x}\right)$$ which simplifies to $$1.09 = \log\left(\frac{6}{0.03x}\right)$$ 3. **Recall the logarithm rule:** If $\log(a) = b$, then $a = 10^b$. Apply this to get $$\frac{6}{0.03x} = 10^{1.09}$$ 4. **Calculate $10^{1.09}$:** $$10^{1.09} \approx 12.3$$ 5. **Solve for $x$:** $$\frac{6}{0.03x} = 12.3 \implies 0.03x = \frac{6}{12.3}$$ $$x = \frac{6}{12.3 \times 0.03}$$ 6. **Simplify the denominator:** $$12.3 \times 0.03 = 0.369$$ 7. **Final calculation:** $$x = \frac{6}{0.369} \approx 16.26$$ **Answer:** $x \approx 16.26$