To simplify $\frac{\log(125)}{\log(\sqrt{5})}$, let's break it down step by step:

1. Express the numbers in terms of powers of 5:

   • $125 = 5^3$
   • $\sqrt{5} = 5^{1/2}$

2. Apply logarithmic properties: Using the power rule of logarithms, $\log(a^b) = b \log(a)$, we can simplify both the numerator and the denominator.

   • $\log(125) = \log(5^3) = 3 \log(5)$
   • $\log(\sqrt{5}) = \log(5^{1/2}) = \frac{1}{2} \log(5)$

3. Substitute these values back into the original expression: $\frac{\log(125)}{\log(\sqrt{5})} = \frac{3 \log(5)}{\frac{1}{2} \log(5)}$

4. Simplify: Cancel out $\log(5)$ from the numerator and the denominator: $\frac{3 \log(5)}{\frac{1}{2} \log(5)} = \frac{3}{\frac{1}{2}} = 3 \times 2 = 6$

Thus, the simplified value is:

$\boxed{6}$

Would you like further explanation, or do you have any questions about this process?

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Here are five related questions:

1. How would you simplify $\frac{\log(1000)}{\log(10)}$?
2. Can you explain how to use the change of base formula for logarithms?
3. What is $\log_b(a^n)$ in terms of simpler logarithmic expressions?
4. How does the logarithmic property $\log(a \cdot b) = \log(a) + \log(b)$ apply in calculations?
5. What is the value of $\log(1)$ and why?

Tip: Remember that logarithmic rules apply to any base, not just base 10, as long as the base is consistent.