Processing Math: 48%
3.3 Exercises
From Förberedande kurs i matematik 1
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===Exercise 3.3:1=== | ===Exercise 3.3:1=== | ||
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Revision as of 20:47, 28 October 2008
| Theory | Exercises |
Exercise 3.3:1
Solve the following equations for
| a) | | b) | |
| c) | | d) | |
Answer | Solution a | Solution b | Solution c | Solution d
Loading...Exercise 3.3:2
Calculate
| a) | | b) | | c) | | d) | |
| e) | | f) | | g) | | h) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution g | Solution h
Exercise 3.3:3
Calculate
| a) | | b) | | c) | |
| d) | \displaystyle \log_3{\left(9\cdot3^{1/3}\right)} | e) | \displaystyle 2^{\log_{\scriptstyle2}{4}} | f) | \displaystyle \log_2{4}+\log_2{\displaystyle \frac{1}{16}} |
| g) | \displaystyle \log_3{12}-\log_3{4} | h) | \displaystyle \log_a{\bigl(a^2\sqrt{a}\,\bigr)} |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution g | Solution h
Exercise 3.3:4
Simplify
| a) | \displaystyle \lg{50}-\lg{5} | b) | \displaystyle \lg{23}+\lg{\displaystyle \frac{1}{23}} | c) | \displaystyle \lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}} |
Answer | Solution a | Solution b | Solution c
Exercise 3.3:5
Simplify
| a) | \displaystyle \ln{e^3}+\ln{e^2} | b) | \displaystyle \ln{8}-\ln{4}-\ln{2} | c) | \displaystyle (\ln{1})\cdot e^2 |
| d) | \displaystyle \ln{e}-1 | e) | \displaystyle \ln{\displaystyle \frac{1}{e^2}} | f) | \displaystyle \left(e^{\ln{e}}\right)^2 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 3.3:6
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Use the calculator on the right to calculate the following to three decimal places. (The button LN signifies the natural logarithm with base e):
|
Answer | Solution a | Solution b | Solution c
