To solve the inequality by graphing, we first have to create functions using the inequality's left-hand and right-hand sides.
y=log(x)+3log(x-1) and y=4
To enter them in your calculator, push Y= and write them in the first two rows.
With our functions entered, we can push GRAPH to draw them.
The windows settings do not show the intersection point, so let's push WINDOW and change the settings of the x-axis.
We can see that there is one point of intersection. To find this point, we can use the intersect option. Push 2nd and TRACE, then choose the list's fifth option. Now we have to select the two graphs and provide the calculator with a guess of where the intersection might be.
The graphs intersect at x≈ 10.76. Now we have to identify the x-values that make the inequality true. We are looking for x-values that correspond to y-values of y=log(x)+3log(x-1) that are less than 4. From the graph, we see that this happens before the intersection point. This tells us the upper bound of the solution set.
x < 10.76
Because logarithmic functions always have a domain of only positive numbers, we know that our solution set will only contain values greater than 0. Combining these two pieces of information, we get the complete solution set for the inequality.
0 < x <10.76
