To simplify the given expression:

$\frac{-1\log a}{-1\log g}$

We can follow these steps:

1. The negative signs in both the numerator and denominator can cancel each other out:

$\frac{-1\log a}{-1\log g} = \frac{\log a}{\log g}$

2. The expression $\frac{\log a}{\log g}$ can be rewritten using the change of base formula for logarithms. This states that:

$\frac{\log a}{\log g} = \log_g a$

Thus, the simplified form of the expression is:

$\log_g a$

Would you like further details on the logarithmic properties, or do you have any other questions?

---

Here are five related questions to expand on this:

1. How can you derive the change of base formula for logarithms?
2. What happens when the base $g$ equals $a$?
3. How would you simplify $\frac{\log_g(a^2)}{\log_g(a^3)}$?
4. What is the value of $\log_2 8$?
5. How does the logarithmic property $\log_b(xy) = \log_b(x) + \log_b(y)$ work?

Tip: When simplifying logarithmic expressions, always check for negative signs and see if properties like change of base can help!