1. The problem is to evaluate $\log\left(\frac{2}{3}\right)$.\n\n2. Recall the logarithm property: $\log\left(\frac{a}{b}\right) = \log(a) - \log(b)$.\n\n3. Applying this property, we get: $$\log\left(\frac{2}{3}\right) = \log(2) - \log(3).$$\n\n4. Without a specified base, the logarithm is typically assumed to be base 10 (common logarithm).\n\n5. Using approximate values: $\log(2) \approx 0.3010$ and $\log(3) \approx 0.4771$.\n\n6. Substitute these values: $$\log\left(\frac{2}{3}\right) \approx 0.3010 - 0.4771 = -0.1761.$$\n\n7. Therefore, the value of $\log\left(\frac{2}{3}\right)$ is approximately $-0.1761$.