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Monday, March 1, 1999 Math 4 Exam 4 Name _______________________ Solve the equations. Give exact answers. 1. x 8⋅3 = 5 (6) 1. ___________________ 2. 1− x e =5 (6) 2. ___________________ 3. log 6 (x + 3)+ log6 (x + 4 )= 1 (6) 3. ___________________ 4. (6) 3log 2 x = − log 2 27 4. ___________________ Solve the system of equations. 5. 3x − y = − 2 2x 2 − y = 0 (10) 5. ___________________ x+ y 6. =5 y− z= 2 x+ z=3 (10) 6. ___________________ 7. (4) Use your calculator to solve the following equation. Round your answer to three decimal places. x 2 =5 7. ___________________ 8. (6) Write the expression as a sum, difference and/or multiple of logarithms. x3 y log 2z 2 ___________________ 9. (6) Rewrite as logarithm of single quantity 2 3log a x + 12 log a x + 1 − 4 log a (x + 1) ( ) ___________________ For problems 10-17, match the function with the proper graph. (16) _____10. y = log 3 x _____14. y = − log 3 x _____11. y = log 3 x − 1 _____15. y = log 3 (1 − x ) _____12. y = log 3 (− x ) _____16. y = − log 3 (− x ) _____13. y = log 3 (x − 1) _____17. y = 1− log3 x 18. Evaluate 3ln 29 to nearest 3 decimal places. ln 7 − ln 2 (6) 19. Sketch the graph of f (x ) = 3x + 1 − 2 . State domain and range (10) 4 2 -4 -2 2 4 -2 -4 domain ___________________ range ___________________ 20. Graph the system. (8) x 2 + y 2 ≤16 x2 + y ≥ 2