Use the graph of $f(x)=\log _{2} x$ to graph the function $f(x)=\log _{2}(x-1)+4$
Answer
\(\boxed{\text{The graph of the function } f(x)=\log _{2}(x-1)+4 \text{ is the graph of } f(x)=\log _{2} x \text{ shifted one unit to the right and four units up.}}\)
Step 1 ：The function \(f(x)=\log _{2}(x-1)+4\) is a transformation of the function \(f(x)=\log _{2} x\). Specifically, the graph of \(f(x)=\log _{2}(x-1)+4\) is the graph of \(f(x)=\log _{2} x\) shifted one unit to the right and four units up.
Step 2 ：To graph this function, we generate a range of x values, compute the corresponding y values using the function \(f(x)=\log _{2}(x-1)+4\), and then plot these points.
Step 3 ：\(\boxed{\text{The graph of the function } f(x)=\log _{2}(x-1)+4 \text{ is the graph of } f(x)=\log _{2} x \text{ shifted one unit to the right and four units up.}}\)
