1. The problem is to simplify the expression $\log(105) - \log(105)$.\n\n2. We use the logarithmic property: $\log(a) - \log(b) = \log\left(\frac{a}{b}\right)$. This means subtracting two logarithms with the same base is equivalent to the logarithm of the division of their arguments.\n\n3. Applying the property, we get: $$\log(105) - \log(105) = \log\left(\frac{105}{105}\right)$$\n\n4. Simplify the fraction inside the logarithm: $$\log\left(\frac{\cancel{105}}{\cancel{105}}\right) = \log(1)$$\n\n5. We know that $\log(1) = 0$ for any logarithm base (except base 1, which is undefined).\n\n6. Therefore, the simplified value of the expression is $0$.