Example 2

Solve log x + 2 log ( x + 1 ) < 2 log x plus 2 log open x plus 1 close less than 2  using a table.

Step 1 Define Y1 and Y2.

The solution is 0 < x < 4 . 0 less than x less than 4 .

Step 2 Make a table and examine the values.

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Step 3 Identify the x-values that make the inequality true.

Exercises

Solve each inequality using a table. (Hint: For more accurate results, set Δ Tbl = 0.001 . cap delta cap tbl equals , 0.001 , . )

12. log x + log ( x + 1 ) < 3 log x plus log open x plus 1 close less than 3
13. 3 ( 2 ) x + 1 > 5 3 . open 2 close super x plus 1 end super . greater than 5
14. log x + 5 log ( x − 1 ) ≥ 3 log x plus 5 log open x minus 1 close greater than or equal to 3
15. 5 ( 3 ) x ≤ 2 5 . open 3 close to the x . less than or equal to 2
16. 3 log x + log ( x + 2 ) > 1 3 log x plus log open x plus 2 close greater than 1
17. 2 ( 4 ) x + 3 ≤ 8 2 . open 4 close super x plus 3 end super . less than or equal to 8

Barometric Pressure Average barometric pressure varies with the altitude of a location. The greater the altitude is, the lower the pressure. The altitude A is measured in feet above sea level. The barometric pressure P is measured in inches of mercury (in. Hg). The altitude can be modeled by the function A ( P ) = 90 , 000 − 26 , 500 ln P . eh open p close equals 90 comma 000 minus 26 comma 500 , ln p .

18. What is a reasonable domain of the function? What is the range of the function?
19. Graphing Calculator Use a graphing calculator to make a table of function values. Use TblStart = 30 and Δ Tbl = − 1 . cap delta cap tbl equals negative 1 .
20. Write an equation to find what average pressure the model predicts at sea level, or A = 0. eh equals 0.  Use your table to solve the equation.
21. Kilimanjaro is a mountain in Tanzania that formed from three extinct volcanoes. The base of the mountain is at 3000 ft above sea level. The peak is at 19,340 ft above sea level. On Kilimanjaro, 3000 ≤ A ( P ) ≤ 19 , 340 3000 , less than or equal to eh open p close less than or equal to 19 comma 340  is true for the altitude. Write an inequality from which you can find minimum and maximum values of normal barometric pressure on Kilimanjaro. Use a table and solve the inequality for P.
22. Denver, Colorado, is nicknamed the “Mile High City” because its elevation is about 1 mile, or 5280 ft, above sea level. The lowest point in Phoenix, Arizona, is 1117 ft above sea level. Write an inequality that describes the range of A(P) as you drive from Phoenix to Denver. Then solve the inequality for P. (Assume that you never go lower than 1117 ft and you never go higher than 5280 ft.)

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