Processing Math: 48%
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

3.3 Exercises

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
Current revision (20:49, 28 October 2008) (edit) (undo)
 
(20 intermediate revisions not shown.)
Line 2: Line 2:
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
| style="border-bottom:1px solid #000" width="5px" |  
| style="border-bottom:1px solid #000" width="5px" |  
-
{{Mall:Ej vald flik|[[3.3 Logaritmer|Teori]]}}
+
{{Not selected tab|[[3.3 Logarithms|Theory]]}}
-
{{Mall:Vald flik|[[3.3 Övningar|Övningar]]}}
+
{{Selected tab|[[3.3 Exercises|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
| style="border-bottom:1px solid #000" width="100%"|  
|}
|}
-
 
+
===Exercise 3.3:1===
-
===Övning 3.3:1===
+
<div class="ovning">
<div class="ovning">
-
Best&auml;m <math>\,x\,</math> om
+
Solve the following equations for <math>x</math>.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="50%" | <math>10^x=1\,000</math>
|width="50%" | <math>10^x=1\,000</math>
|b)
|b)
-
|width="50%" | <math>10^x=0{,}1</math>
+
|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{,}000\,1</math>
+
|width="50%" | <math>\displaystyle \frac{1}{10^x}=0\textrm{.}000\,1</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:1|Lösning a|Lösning 3.3:1a|Lösning b|Lösning 3.3:1b|Lösning c|Lösning 3.3:1c|Lösning d|Lösning 3.3:1d}}
+
</div>{{#NAVCONTENT:Answer|Answer 3.3:1|Solution a|Solution 3.3:1a|Solution b|Solution 3.3:1b|Solution c|Solution 3.3:1c|Solution d|Solution 3.3:1d}}
-
===Övning 3.3:2===
+
===Exercise 3.3:2===
<div class="ovning">
<div class="ovning">
-
Ber&auml;kna
+
Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
-
|width="25%" | <math>\lg{ 0{,}1}</math>
+
|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{,}001}</math>
+
|width="25%" | <math>\lg {0\textrm{.}001}</math>
|d)
|d)
|width="25%" | <math>\lg {1}</math>
|width="25%" | <math>\lg {1}</math>
Line 43: Line 42:
|width="25%" | <math>\lg{10^3}</math>
|width="25%" | <math>\lg{10^3}</math>
|g)
|g)
-
|width="25%" | <math>10^{-\lg{0{,}1}}</math>
+
|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>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:2|Lösning a|Lösning 3.3:2a|Lösning b|Lösning 3.3:2b|Lösning c|Lösning 3.3:2c|Lösning d|Lösning 3.3:2d|Lösning e|Lösning 3.3:2e|Lösning f|Lösning 3.3:2f|Lösning g|Lösning 3.3:2g|Lösning h|Lösning 3.3:2h}}
+
</div>{{#NAVCONTENT:Answer|Answer 3.3:2|Solution a|Solution 3.3:2a|Solution b|Solution 3.3:2b|Solution c|Solution 3.3:2c|Solution d|Solution 3.3:2d|Solution e|Solution 3.3:2e|Solution f|Solution 3.3:2f|Solution g|Solution 3.3:2g|Solution h|Solution 3.3:2h}}
-
===Övning 3.3:3===
+
===Exercise 3.3:3===
<div class="ovning">
<div class="ovning">
-
Ber&auml;kna
+
Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 58: Line 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{,}125}</math>
+
|width="33%" | <math>\log_2{0\textrm{.}125}</math>
|-
|-
|d)
|d)
Line 72: Line 71:
|width="33%" | <math>\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</math>
|width="33%" | <math>\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:3|Lösning a|Lösning 3.3:3a|Lösning b|Lösning 3.3:3b|Lösning c|Lösning 3.3:3c|Lösning d|Lösning 3.3:3d|Lösning e|Lösning 3.3:3e|Lösning f|Lösning 3.3:3f|Lösning g|Lösning 3.3:3g|Lösning h|Lösning 3.3:3h}}
+
</div>{{#NAVCONTENT:Answer|Answer 3.3:3|Solution a|Solution 3.3:3a|Solution b|Solution 3.3:3b|Solution c|Solution 3.3:3c|Solution d|Solution 3.3:3d|Solution e|Solution 3.3:3e|Solution f|Solution 3.3:3f|Solution g|Solution 3.3:3g|Solution h|Solution 3.3:3h}}
-
===Övning 3.3:4===
+
===Exercise 3.3:4===
<div class="ovning">
<div class="ovning">
-
F&ouml;renkla
+
Simplify
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 85: Line 84:
|width="33%" | <math>\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</math>
|width="33%" | <math>\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:4|Lösning a|Lösning 3.3:4a|Lösning b|Lösning 3.3:4b|Lösning c|Lösning 3.3:4c}}
+
</div>{{#NAVCONTENT:Answer|Answer 3.3:4|Solution a|Solution 3.3:4a|Solution b|Solution 3.3:4b|Solution c|Solution 3.3:4c}}
-
===Övning 3.3:5===
+
===Exercise 3.3:5===
<div class="ovning">
<div class="ovning">
-
F&ouml;renkla
+
Simplify
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 105: Line 104:
|width="33%" | <math>\left(e^{\ln{e}}\right)^2</math>
|width="33%" | <math>\left(e^{\ln{e}}\right)^2</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:5|Lösning a|Lösning 3.3:5a|Lösning b|Lösning 3.3:5b|Lösning c|Lösning 3.3:5c|Lösning d|Lösning 3.3:5d|Lösning e|Lösning 3.3:5e|Lösning f|Lösning 3.3:5f}}
+
</div>{{#NAVCONTENT:Answer|Answer 3.3:5|Solution a|Solution 3.3:5a|Solution b|Solution 3.3:5b|Solution c|Solution 3.3:5c|Solution d|Solution 3.3:5d|Solution e|Solution 3.3:5e|Solution f|Solution 3.3:5f}}
-
===Övning 3.3:6===
+
===Exercise 3.3:6===
<div class="ovning">
<div class="ovning">
-
{{LOGCALCULATOR}}
+
{| width="100%"
-
Anv&auml;nd minir&auml;knaren till h&ouml;ger f&ouml;r att ber&auml;kna med tre decimaler (Knappen <tt>LN</tt> betecknar den naturliga logaritmen i basen ''e''):
+
| width="100%" |
 +
Use the calculator on the right to calculate the following to three decimal places. The button <tt>LN</tt> signifies the natural logarithm with base ''e''.
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
Line 121: Line 121:
|width="100%" | <math>\log_3{\log_2{(3^{118})}}</math>
|width="100%" | <math>\log_3{\log_2{(3^{118})}}</math>
|}
|}
-
</div>{{#NAVCONTENT:Svar|Svar 3.3:6|Lösning a|Lösning 3.3:6a|Lösning b|Lösning 3.3:6b|Lösning c|Lösning 3.3:6c}}
+
||{{LOGCALCULATOR}}
 +
|}
 +
</div>{{#NAVCONTENT:Answer|Answer 3.3:6|Solution a|Solution 3.3:6a|Solution b|Solution 3.3:6b|Solution c|Solution 3.3:6c}}

Current revision

       Theory          Exercises      


Exercise 3.3:1

Solve the following equations for x.

a) 10x=1000 b) 10x=0.1
c) 110x=100 d) 110x=0.0001

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 3.3:2

Calculate

a) lg0.1 b) lg10000 c) lg0.001 d) lg1
e) 10lg2 f) lg103 g) 10−lg0.1 h) lg1102

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution g | Solution h

Exercise 3.3:3

Calculate

a) log28 b) log931 c) log20.125
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}}

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

Use the calculator on the right to calculate the following to three decimal places. The button LN signifies the natural logarithm with base e.

a) \displaystyle \log_3{4}
b) \displaystyle \lg{46}
c) \displaystyle \log_3{\log_2{(3^{118})}}





Answer | Solution a | Solution b | Solution c

Retrieved from "http://wiki.math.se/wikis/2009/bridgecourse1-ImperialCollege/index.php/3.3_Exercises"