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3.3 Exercises

From Förberedande kurs i matematik 1

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|width="50%" | <math>\displaystyle \frac{1}{10^x}=0\textrm{.}000\,1</math>
|width="50%" | <math>\displaystyle \frac{1}{10^x}=0\textrm{.}000\,1</math>
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</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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</div>{{#NAVCONTENT:Answer|Answer 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}}
===Exercise 3.3:2===
===Exercise 3.3:2===
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|width="25%" | <math>\lg{\displaystyle \frac{1}{10^2}}</math>
|width="25%" | <math>\lg{\displaystyle \frac{1}{10^2}}</math>
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</div>{{#NAVCONTENT:Answer|Svar 3.3:2|Solution a|Lösning 3.3:2a|Solution b|Lösning 3.3:2b|Solution c|Lösning 3.3:2c|Solution d|Lösning 3.3:2d|Solution e|Lösning 3.3:2e|Solution f|Lösning 3.3:2f|Solution g|Lösning 3.3:2g|Solution h|Lösning 3.3:2h}}
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</div>{{#NAVCONTENT:Answer|Answer 3.3:2|Solution a|Lösning 3.3:2a|Solution b|Lösning 3.3:2b|Solution c|Lösning 3.3:2c|Solution d|Lösning 3.3:2d|Solution e|Lösning 3.3:2e|Solution f|Lösning 3.3:2f|Solution g|Lösning 3.3:2g|Solution h|Lösning 3.3:2h}}
===Exercise 3.3:3===
===Exercise 3.3:3===
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|width="33%" | <math>\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</math>
|width="33%" | <math>\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</math>
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</div>{{#NAVCONTENT:Answer|Svar 3.3:3|Solution a|Lösning 3.3:3a|Solution b|Lösning 3.3:3b|Solution c|Lösning 3.3:3c|Solution d|Lösning 3.3:3d|Solution e|Lösning 3.3:3e|Solution f|Lösning 3.3:3f|Solution g|Lösning 3.3:3g|Solution h|Lösning 3.3:3h}}
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</div>{{#NAVCONTENT:Answer|Answer 3.3:3|Solution a|Lösning 3.3:3a|Solution b|Lösning 3.3:3b|Solution c|Lösning 3.3:3c|Solution d|Lösning 3.3:3d|Solution e|Lösning 3.3:3e|Solution f|Lösning 3.3:3f|Solution g|Lösning 3.3:3g|Solution h|Lösning 3.3:3h}}
===Exercise 3.3:4===
===Exercise 3.3:4===
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|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>
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</div>{{#NAVCONTENT:Answer|Svar 3.3:4|Solution a|Lösning 3.3:4a|Solution b|Lösning 3.3:4b|Solution c|Lösning 3.3:4c}}
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</div>{{#NAVCONTENT:Answer|Answer 3.3:4|Solution a|Lösning 3.3:4a|Solution b|Lösning 3.3:4b|Solution c|Lösning 3.3:4c}}
===Exercise 3.3:5===
===Exercise 3.3:5===
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|width="33%" | <math>\left(e^{\ln{e}}\right)^2</math>
|width="33%" | <math>\left(e^{\ln{e}}\right)^2</math>
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</div>{{#NAVCONTENT:Answer|Svar 3.3:5|Solution a|Lösning 3.3:5a|Solution b|Lösning 3.3:5b|Solution c|Lösning 3.3:5c|Solution d|Lösning 3.3:5d|Solution e|Lösning 3.3:5e|Solution f|Lösning 3.3:5f}}
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</div>{{#NAVCONTENT:Answer|Answer 3.3:5|Solution a|Lösning 3.3:5a|Solution b|Lösning 3.3:5b|Solution c|Lösning 3.3:5c|Solution d|Lösning 3.3:5d|Solution e|Lösning 3.3:5e|Solution f|Lösning 3.3:5f}}
===Exercise 3.3:6===
===Exercise 3.3:6===
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</div>{{#NAVCONTENT:Answer|Svar 3.3:6|Solution a|Lösning 3.3:6a|Solution b|Lösning 3.3:6b|Solution c|Lösning 3.3:6c}}
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</div>{{#NAVCONTENT:Answer|Answer 3.3:6|Solution a|Lösning 3.3:6a|Solution b|Lösning 3.3:6b|Solution c|Lösning 3.3:6c}}

Revision as of 07:09, 9 September 2008

       Theory          Exercises      


Exercise 3.3:1

What is x if

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

Exercise 3.3:2

Calculate

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

Exercise 3.3:3

Calculate

a) log28 b) log931 c) log20.125
d) log39313  e) 2log24 f) log24+log2116
g) log312log34 h) logaa2a 

Exercise 3.3:4

Simplify

a) lg50lg5 b) lg23+lg123 c) lg2713+2lg3+lg91

Exercise 3.3:5

Simplify

a) lne3+lne2 b) ln8ln4ln2 c) (ln1)e2
d) lne1 e) ln1e2 f) elne2 

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) log34
b) lg46
c) \displaystyle \log_3{\log_2{(3^{118})}}