Math Problem Statement

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

(0, ∞), (-∞, ∞) b.

(-∞, ∞), (0, ∞) c.

(0, ∞), (0, ∞) d.

(-∞, ∞), (-∞, ∞)

Solution

For the function y=log6(x)y = \log_6(x):

  1. Domain: Since the logarithmic function is only defined for positive values of xx, the domain is (0,)(0, \infty).
  2. Range: The range of a logarithmic function, such as y=log6(x)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,),(,)(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)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(x3)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 logb(x)\log_b(x) to be defined, xx must be positive.

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Math Problem Analysis

Mathematical Concepts

Logarithmic Functions
Domain and Range

Formulas

y = log_b(x)

Theorems

Domain and Range of Logarithmic Functions

Suitable Grade Level

Grades 9-11