Question

what is the range of \\(y = \log_{8} x\\)?

• all real numbers less than 0
• all real numbers greater than 0
• all real numbers not equal to 0
• all real numbers

Explanation:

Analyze the logarithmic function

Using the Range of Logarithmic Functions knowledge point

$$ y = \log_{8}(x) $$

The domain of this parent logarithmic function is \(x \in (0, \infty)\).

Determine the range of the function

Using the Range of Logarithmic Functions knowledge point

$$ \text{Range} = (-\infty, \infty) $$

This means the output \(y\) can take any real value, which corresponds to "all real numbers".

Answer:

• all real numbers less than 0
• all real numbers greater than 0
• all real numbers not equal to 0
• all real numbers (Correct answer)