7.2.1 Exponential and Logarithmic Equations and Inequalities − Worksheet
Example 1: Solve and check. 1. = 4 32 x 2 1 2
2. 9 x = 3 x − 2
3. 2 x = 4 x + 1
x
x
2
=
1 4
1 2
4. 4 x = 10
5.
6. 2.4 3 x + 1 = 9
Example 2: 7. The population of a small coastal resort town, currently 3400, grows at a rate of 3% per year. This growth can be expressed by the exponential equation P = 3400(l + 0.03) t , where P is the population after t years. Find the number of years it will take for the population to exceed 10,000 people.
Example 3: Solve. 8. log 2 (7 x + 1) = log 2 (2 − x )
9. log 6 (2 x + 3) = 3
=
x
2
10.
11. log 3 x
9 = 12
− log72 log
0
3
x 3
=
x 2
12.
13.
− = x log (3 4 ) log
+ log50 log
2
7
7
+ + =
3 10
14. log x + log( x + 48) = 2
15.
log( x ) + 1 = 0 log 1 0
x log
+
Example 4: Use a table and graph to solve. 16. 2 2 x + 1 = 256
17. 2 x 3 x ≤ 7776
18. 2log x 4 = 16
19. x > 10log x
130
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