Question: User: if i get something like log a (1/4) can it also be written as -log a (4)?
1. **Problem Statement:**
We want to verify if the logarithmic expression $\log_a \left( \frac{1}{4} \right)$ can be rewritten as $-\log_a (4)$.
2. **Relevant Formula:**
The logarithm of a reciprocal can be expressed using the property:
$$\log_a \left( \frac{1}{x} \right) = -\log_a (x)$$
This is because:
$$\log_a \left( \frac{1}{x} \right) = \log_a (1) - \log_a (x)$$
and since $\log_a (1) = 0$, it simplifies to:
$$-\log_a (x)$$
3. **Applying the formula:**
Substitute $x = 4$:
$$\log_a \left( \frac{1}{4} \right) = -\log_a (4)$$
4. **Explanation:**
This means that the logarithm of the reciprocal of a number is the negative of the logarithm of the number itself.
5. **Conclusion:**
Yes, $\log_a \left( \frac{1}{4} \right)$ can indeed be written as $-\log_a (4)$.
**Final answer:**
$$\log_a \left( \frac{1}{4} \right) = -\log_a (4)$$