TEST 5-REVIEW
Determine whether the function is invertible. If it is, find the inverse.
1) {(5, -5), (6, -5), (7, -2), (8, -4)}
Answer: Not invertible
2) {(-1, -3), (1, 3), (9, 5), (-9, -5)}
Answer: {(-3, -1), (3, 1), (5, 9), (-5, -9)}
Find the inverse of the function.
3) f(x) = 3x + 6
x-6
Answer: f-1 (x) =
3
Decide whether or not the functions are inverses of each other.
x+5
4) f(x) = 5x - 4, g(x) =
4
Answer: No
Graph the function.
5) f(x) = 5 x
Answer:
1
Solve the equation.
6) 2(12 - 3x) = 64
Answer: {2}
1
7) 3(6 - 3x) =
27
Answer: {3}
Simplify the expression.
8) ln (e6)
Answer: 6
9) 4
log4 (8x)
Answer: 8x
Graph the function.
10) y = log4 x
Answer:
2
If a logarithmic equation is given, then rewrite it as an equivalent exponential equation. If an exponential equation is
given, then rewrite it as an equivalent logarithmic equation.
11) 73 = 343
Answer: log7 (343) = 3
12) ln x = 8
Answer: x = e8
13) log9 (729) = 3
Answer: 93 = 729
Rewrite the expression as a single logarithm.
14) 6 logm p - 5 logm q2
p6
q10
Answer: logm
15) 3 logb (7) - logb (3)
Answer: logb
343
3
16) 6 log2 (6x - 3) + 5 log2 (4x + 3)
Answer: log2 ((6x - 3)6(4x + 3)5)
Rewrite the expression as a sum or difference of logarithms or multiples of logarithms.
x 8 y3
17) log2
4
Answer: 8 log2 (x) + 3 log2 (y) - log2 (4)
Use a calculator and the base-change formula to find the logarithm to four decimal places.
18) log8 (66.71)
Answer: 2.0199
Solve the equation. Round your answer to three decimal places.
19) 5x = 22
Answer: 1.921
20) 5(3x - 2) = 20
Answer: 1.287
3
21) logx (3.1) = -3.7
Answer: 0.737
Solve the equation. Give an exact solution.
22) ln(2x - 3) = ln 9 - ln (x - 3)
Answer:
9
2
23) log4 (x - 6) + log4 (x - 6) = 1
Answer: 8
24) ln eln x - ln(x - 3) = ln 8
Answer:
24
7
Solve the equation. If necessary, round to thousandths.
25) 3e6x - 2 = 18
Answer: 0.632
Solve the problem.
26) An initial investment of $14,000 is appreciated for 14 years in an account that earns 8% interest, compounded
semiannually. Find the amount of money in the account at the end of the period.
Answer: $41,981.85
27) What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two
decimal places.
Answer: $864.12
Solve the system.
28) x2 + y2 = 25
x-y=1
Answer: {(4, 3), (-3, -4)}
29) y = x2 - 6x + 9
x+ y=3
Answer: {(2, 1), (3, 0)}
30) 3x2 - 3y2 = -48
5x2 + 2y2 = 95
Answer: {(3, 5), (-3, 5), (3, -5), (-3, -5)}
4