The domain of `y=log_(x)5` is :

Options

A. `x gt5`
B. `(0, oo)`
C. `(0, oo)~{1}`
D. `[5, oo)`

Answer

To find the domain of the function \( y = \log_{x}(5) \), we need to consider the properties of logarithms. The logarithm is defined under certain conditions that we must satisfy.

### Step-by-Step Solution:

1. **Identify the Base of the Logarithm**:
The base of the logarithm is \( x \). For the logarithm to be defined, the base must be greater than 0 and cannot be equal to 1.
\[ x > 0 \quad \text{and} \quad x \neq 1 \]

2. **Combine the Conditions**:
From the above conditions, we can combine them to express the domain. The base \( x \) must be positive, and it must not equal 1.
\[ x \in (0, 1) \cup (1, \infty) \]

3. **Conclusion**:
Therefore, the domain of the function \( y = \log_{x}(5) \) is:
\[ (0, 1) \cup (1, \infty) \]

### Final Answer:
The domain of \( y = \log_{x}(5) \) is \( (0, 1) \cup (1, \infty) \).

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