103b
Algebra II
Review: Exponents and Logarithms
Extra Practice
1.
Name________________________
Date___________ Per __________
Optional Review
Apply the properties of exponents to rewrite each expression in the form 𝑘𝑥 𝑛 or 𝑘𝑒 𝑛 .
a.
3
2 2
3
(5𝑥 −5 )(−2𝑥 4 )(−3𝑥)2
2𝑥 4
−4
d. (9𝑥 −1 )
c. (
b. (64𝑒 )
e.
𝟑
64𝒙9
√
1
3
𝑒 2 )−3
f. (42−√7 ) (42+√7 )
27
2. Evaluate each expression for 𝐴 = 216 and 𝐵 = 25.
𝟒
𝟑
a. 𝑨𝟑 ∙ 𝑩𝟐
𝟑
b. ( √𝑨 + √𝑩)
−𝟏
3. Solve for x and check:
3
a) −2𝑥 2 + 6 = −48
5
b) 𝑥 4 − 3 = 240
Simplify each to an expression that contains only one base-10 logarithm.
4. log 8 (1,000)
5. log 5 (0.025)
6. log 6 (0.6)
Expand each expression.
𝑡3
7. log(𝑧√𝑥𝑦)
8. log 7 ( 𝑏 )
Condense each expression.
9.
1
2ln(𝑎) + 2ln(𝑣) + 4 ln(𝑓) − ln(𝑧)
10. log(𝑚) − 5log(𝑝) −
log(𝑎)
3
Solve each equation for x. Write your answer as a simplified base-10 logarithm and write your answer as a decimal
rounded to the nearest thousandth. Check your solution using your calculator.
11. −2 − 18𝑥 = −7
1
12. 11𝑥−8 − 5 = 54
13. 54𝑥−3 = 125
14.
(20)−6𝑥 + 6 = 55
Solve each equation and check.
15. ln(𝑥12 ) = 144
16. log(𝑥) − log(2) = 1
17. 𝑙𝑜𝑔12 (𝑥 2 + 35) = 𝑙𝑜𝑔12 (−12𝑥 − 1)
18. log 2 (5𝑥 + 2) − log 2 (𝑥 − 4) = 2