Download ( )+ log6 x + 4

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