Problem 93
Question
Explain how to find the domain of a logarithmic function.
Step-by-Step Solution
Verified Answer
The domain of a logarithmic function is all real numbers greater than zero.
1Step 1: Understand the Function
First, one must understand what a logarithmic function is. It is the inverse of an exponential function. The notation is \(y = \log_{b}(x)\), where b is the base of the logarithm.
2Step 2: Identify the Constraints
The logarithmic functions are undefined for values of x that are less than or equal to zero. This is because logarithms represent the exponent to which the base must be raised to get the argument. There is no exponent that you can raise a positive number to that will result in zero or a negative number.
3Step 3: Set the Domain
Given the constraints, the domain of a logarithmic function is all real numbers greater than zero. This can be expressed in interval notation as \(x > 0\) or in set notation as \{x ∈ ℝ: x > 0\}.
Other exercises in this chapter
Problem 92
Explain how to use the graph of \(f(x)=2^{x}\) to obtain the graph of \(g(x)=\log _{2} x.\)
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