Use the guided visualization to answer the question.
Click here to open the guided visualization.
Set the values of to 1 , a to 2 , to 0 , and to 0 . Use the slider to adjust the value of from -3 to 3 and pay attention
to the equation of the logarithmic function. Note the domain for each value of . Based on what you observe, what
would the domain of be?
The domain of would be

Ask by Chambers Gordon. in the United States

Mar 26,2025

Question

Use the guided visualization to answer the question.
Click here to open the guided visualization.
Set the values of to 1 , a to 2 , to 0 , and to 0 . Use the slider to adjust the value of from -3 to 3 and pay attention
to the equation of the logarithmic function. Note the domain for each value of . Based on what you observe, what
would the domain of be?
The domain of would be

Ask by Chambers Gordon. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1. The given function is  
   $$
   f(x)=3\log_{2}(x-5).
   $$

2. For a logarithmic function $$\log_b(u)$$ to be defined, the argument $$u$$ must be positive. In this case, the argument is $$x-5$$. Therefore, we require that  
   $$
   x-5 > 0.
   $$

3. Solve the inequality:  
   $$
   \begin{aligned}
   x-5 &> 0, \
   x &> 5.
   \end{aligned}
   $$

4. Thus, the domain of $$f(x)$$ is all real numbers greater than 5, which in interval notation is  
   $$
   (5, \infty).
   $$
The domain of $$ f(x)=3 \log_{2}(x-5) $$ is all real numbers greater than 5, which is $$ (5, \infty) $$.

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