Math III Unit 4 Review
Name________________________
LT15: Understand algebraically and graphically the relationship between exponential and
logarithmic functions including natural logarithms.
Simplify the following expressions using inverse properties:
1. log 7 7
2x
3. log 3 27 x
1
2. log5
25
x
4. log 3 9 2 x+5
Rewrite the following exponential equations as a logarithmic equation:
5. 6 = 36
6. 5 = 125
7. e = x
8. a = b
2
3
3
x
Rewrite the following logarithmic equations as an exponential equations:
1
= −2
36
9. log 9 81 = 2
10. log 6
11. log5 25 = 2
12. log 3 b = a
13. Given the exponential function f ( x=
) 2 x − 7 , find the restrictions on the domain of the
inverse function.
14. A logarithmic function has a domain of ( −3, ∞ ) and a range of ( −∞, ∞ ) . What is the domain
and range of the inverse function?
LT16: Manipulate logarithmic expressions using properties.
Expend the following expressions using properties of logs.
15. log 3 2 y
17. log 3
7
2
16. log b y 3
18. log b
x2
y2
Condense the following expressions using properties of logs.
19. log 3 y + log 3 5
20. log 3 y − log 3 5
21. 2 log 3 x + 3log 3 y − log 3 z
22. 2 log 3 x − 3log 3 y − log 3 z
23. log 3 x + log 3 ( x + 5)
24. ln 4 + ln 2x
LT17: Solve equations using logarithmic and exponential properties.
Solve the following equations, round to the nearest hundredth if necessary.
25.
23 x+5 − 4 =
4
26.
3e x − 5 =
25
27.
log 2 (2 x − 6) =
4
28.
ln 5 x − ln15 =
ln 4
29.
103 x = 12
30.
log5 x + log5 ( x + 2 ) =
log5 24
31.
log 4 ( x − 4) ( x + 2 ) =
2
32.
2 + ln(3x ) =
5
33.
7 = 3e0.3 x
LT#18 Create, manipulate and solve exponential functions using logarithmic properties
34. A bacteria culture doubles in value every 6 hours. If there are 500 cells present initially,
how many are present after 15?
35. A radio-active substance has a half-life of 20 years. If there are 3000 grams present initially,
how long will it take before there is 750 grams left, round your answer to the nearest whole
number?
36. $2000 is invested in an account earning 4.25% compounded semi-annually. How many
years will it take until the account has over $3000 in it?
37. $2000 is invested in an account earning 4.25% compounded monthly. How many years will
it take until the account has over $3000 in it?
38. $2000 is invested in an account earning 4.25% compounded weekly. How many years will
it take until the account has over $3000 in it?
39. A population is increasing at a continuous rate and is modeled by the equation At = 3000e.01t
a. What will the population be after 5 years?
b. After how many years will the population double?
40. A sum of $5000 deposited 5 years ago is now worth $7325. What was the average annual
rate of interest while the money was on deposit?