3.3 Übungen
Aus Online Mathematik Brückenkurs 1
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|width="50%" | <math>10^x=1\,000</math> | |width="50%" | <math>10^x=1\,000</math> | ||
|b) | |b) | ||
| - | |width="50%" | <math>10^x=0{ | + | |width="50%" | <math>10^x=0\textrm{.}1</math> |
|- | |- | ||
|c) | |c) | ||
|width="50%" | <math>\displaystyle \frac{1}{10^x}=100</math> | |width="50%" | <math>\displaystyle \frac{1}{10^x}=100</math> | ||
|d) | |d) | ||
| - | |width="50%" | <math>\displaystyle \frac{1}{10^x}=0{ | + | |width="50%" | <math>\displaystyle \frac{1}{10^x}=0\textrm{.}000\,1</math> |
|} | |} | ||
</div>{{#NAVCONTENT:Answer|Svar 3.3:1|Solution a|Lösning 3.3:1a|Solution b|Lösning 3.3:1b|Solution c|Lösning 3.3:1c|Solution d|Lösning 3.3:1d}} | </div>{{#NAVCONTENT:Answer|Svar 3.3:1|Solution a|Lösning 3.3:1a|Solution b|Lösning 3.3:1b|Solution c|Lösning 3.3:1c|Solution d|Lösning 3.3:1d}} | ||
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{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="25%" | <math>\lg{ 0{ | + | |width="25%" | <math>\lg{ 0\textrm{.}1}</math> |
|b) | |b) | ||
|width="25%" | <math>\lg{ 10\,000}</math> | |width="25%" | <math>\lg{ 10\,000}</math> | ||
|c) | |c) | ||
| - | |width="25%" | <math>\lg {0{ | + | |width="25%" | <math>\lg {0\textrm{.}001}</math> |
|d) | |d) | ||
|width="25%" | <math>\lg {1}</math> | |width="25%" | <math>\lg {1}</math> | ||
| Zeile 42: | Zeile 42: | ||
|width="25%" | <math>\lg{10^3}</math> | |width="25%" | <math>\lg{10^3}</math> | ||
|g) | |g) | ||
| - | |width="25%" | <math>10^{-\lg{0{ | + | |width="25%" | <math>10^{-\lg{0\textrm{.}1}}</math> |
|h) | |h) | ||
|width="25%" | <math>\lg{\displaystyle \frac{1}{10^2}}</math> | |width="25%" | <math>\lg{\displaystyle \frac{1}{10^2}}</math> | ||
| Zeile 57: | Zeile 57: | ||
|width="33%" | <math>\log_9{\displaystyle \frac{1}{3}}</math> | |width="33%" | <math>\log_9{\displaystyle \frac{1}{3}}</math> | ||
|c) | |c) | ||
| - | |width="33%" | <math>\log_2{0{ | + | |width="33%" | <math>\log_2{0\textrm{.}125}</math> |
|- | |- | ||
|d) | |d) | ||
Version vom 11:57, 19. Aug. 2008
Exercise 3.3:1
What is \displaystyle \,x\, if
| a) | \displaystyle 10^x=1\,000 | b) | \displaystyle 10^x=0\textrm{.}1 |
| c) | \displaystyle \displaystyle \frac{1}{10^x}=100 | d) | \displaystyle \displaystyle \frac{1}{10^x}=0\textrm{.}000\,1 |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Exercise 3.3:2
Calculate
| a) | \displaystyle \lg{ 0\textrm{.}1} | b) | \displaystyle \lg{ 10\,000} | c) | \displaystyle \lg {0\textrm{.}001} | d) | \displaystyle \lg {1} |
| e) | \displaystyle 10^{\lg{2}} | f) | \displaystyle \lg{10^3} | g) | \displaystyle 10^{-\lg{0\textrm{.}1}} | h) | \displaystyle \lg{\displaystyle \frac{1}{10^2}} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Solution g
Solution h
Exercise 3.3:3
Calculate
| a) | \displaystyle \log_2{8} | b) | \displaystyle \log_9{\displaystyle \frac{1}{3}} | c) | \displaystyle \log_2{0\textrm{.}125} |
| 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}} |
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):
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