Identify the domain and range of y = log 6(x).
Question 23 Answer
a.

(0, ∞), (-∞, ∞)
b.

(-∞, ∞), (0, ∞)
c.

(0, ∞), (0, ∞)
d.

(-∞, ∞), (-∞, ∞)

For the function \( y = \log_6(x) \):

1. **Domain**: Since the logarithmic function is only defined for positive values of \( x \), the domain is \( (0, \infty) \).
2. **Range**: The range of a logarithmic function, such as \( y = \log_6(x) \), is all real numbers, \( (-\infty, \infty) \), because the output of a logarithmic function can be any real number.

Thus, the correct answer is:

**a. \( (0, \infty), (-\infty, \infty) \)**

Would you like more details on logarithmic domains and ranges? 

Here are 5 related questions:
1. What is the domain and range of \( y = \ln(x) \)?
2. How do you find the domain of a function involving a logarithm?
3. What changes in the domain and range if we use \( y = \log(x - 3) \)?
4. How does the base of the logarithm affect the domain and range?
5. What are the transformations that affect the domain of logarithmic functions?

**Tip:** Remember, for \( \log_b(x) \) to be defined, \( x \) must be positive.

Identify the domain and range of y = log 6(x).

Discover how to determine the domain and range of the logarithmic function y = log6(x). Understand the requirements for a logarithmic function's domain, defined only for positive x-values, and explore how its range covers all real numbers. Suitable for students in Grades 9-11.

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