1. **State the problem:** Solve for $x$ in the equation $7.19 = 6.1 + \log\left(\frac{6}{0.3x}\right)$. 2. **Isolate the logarithm:** Subtract 6.1 from both sides: $$7.19 - 6.1 = \log\left(\frac{6}{0.3x}\right)$$ $$1.09 = \log\left(\frac{6}{0.3x}\right)$$ 3. **Recall the logarithm definition:** If $\log(a) = b$, then $a = 10^b$. So, $$\frac{6}{0.3x} = 10^{1.09}$$ 4. **Calculate $10^{1.09}$:** $$10^{1.09} \approx 12.3$$ 5. **Set up the equation:** $$\frac{6}{0.3x} = 12.3$$ 6. **Solve for $x$:** Multiply both sides by $0.3x$: $$6 = 12.3 \times 0.3x$$ $$6 = 3.69x$$ Divide both sides by 3.69: $$x = \frac{6}{3.69} \approx 1.63$$ **Final answer:** $$x \approx 1.63$$