Which of the following is a logarithmic function?

[tex]y=\log _3 x[/tex]
[tex]y=3^x[/tex]
[tex]y=x+3[/tex]
[tex]y=x^3[/tex]

Identify the general form of a logarithmic function: y = lo g b ​ x .
Compare each given function to the general form.
Recognize that y = lo g 3 ​ x fits the definition of a logarithmic function.
Conclude that the logarithmic function is y = lo g 3 ​ x ​ .

Explanation

Identifying Logarithmic Functions We are given four functions and we need to identify the logarithmic function among them. A logarithmic function has the form y = lo g b ​ x , where b is a positive constant not equal to 1.

Analyzing the Options Let's examine each option:

y = lo g 3 ​ x : This function matches the form of a logarithmic function with base b = 3 .

y = 3 x : This is an exponential function.

y = x + 3 : This is a linear function.

y = x 3 : This is a power function.

Conclusion Therefore, the logarithmic function among the given options is y = lo g 3 ​ x .


Examples
Logarithmic functions are used in many real-world applications, such as measuring the intensity of earthquakes (Richter scale), the loudness of sounds (decibels), and the acidity of solutions (pH scale). They are also used in computer science to analyze the efficiency of algorithms and in finance to model the growth of investments.

Answered by GinnyAnswer | 2025-07-03

The logarithmic function among the given options is y = lo g 3 ​ x . This function fits the general form of logarithmic functions, while the other options are not logarithmic functions. Therefore, the answer is y = lo g 3 ​ x ​ .
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Answered by Anonymous | 2025-07-04