Create functions from the left-hand and right-hand sides of the given inequality, then solve for the point of intersection.
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Practice makes perfect
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)+2log(x-1) and y=1
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.
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≈ 2.87. Notice that we are looking for x-values where the graph y=log(x)+2log(x-1) shows a smaller y-value than 1. From the graph, we see that this happens before the intersection point. Therefore, the solution to the inequality must be 0
