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3.3 Exercises

From Förberedande kurs i matematik 1

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{| 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" |  
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{{Mall:Ej vald flik|[[3.3 Logaritmer|Teori]]}}
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{{Not selected tab|[[3.3 Logarithms|Theory]]}}
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{{Mall:Vald flik|[[3.3 Övningar|Övningar]]}}
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{{Selected tab|[[3.3 Exercises|Exercises]]}}
| style="border-bottom:1px solid #000" width="100%"|  
| style="border-bottom:1px solid #000" width="100%"|  
|}
|}
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===Exercise 3.3:1===
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===Övning 3.3:1===
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<div class="ovning">
<div class="ovning">
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Best&auml;m <math>\,x\,</math> om
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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)
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|width="50%" | <math>10^x=0{,}1</math>
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|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)
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|width="50%" | <math>\displaystyle \frac{1}{10^x}=0{,}000\,1</math>
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|width="50%" | <math>\displaystyle \frac{1}{10^x}=0\textrm{.}000\,1</math>
|}
|}
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</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}}
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</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}}
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{{LOGCALCULATOR}}
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===Exercise 3.3:2===
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<div class="ovning">
 +
Calculate
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{| width="100%" cellspacing="10px"
 +
|a)
 +
|width="25%" | <math>\lg{ 0\textrm{.}1}</math>
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|b)
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|width="25%" | <math>\lg{ 10\,000}</math>
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|c)
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|width="25%" | <math>\lg {0\textrm{.}001}</math>
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|d)
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|width="25%" | <math>\lg {1}</math>
 +
|-
 +
|e)
 +
|width="25%" | <math>10^{\lg{2}}</math>
 +
|f)
 +
|width="25%" | <math>\lg{10^3}</math>
 +
|g)
 +
|width="25%" | <math>10^{-\lg{0\textrm{.}1}}</math>
 +
|h)
 +
|width="25%" | <math>\lg{\displaystyle \frac{1}{10^2}}</math>
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|}
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</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}}
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===Exercise 3.3:3===
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<div class="ovning">
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Calculate
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{| width="100%" cellspacing="10px"
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|a)
 +
|width="33%" | <math>\log_2{8}</math>
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|b)
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|width="33%" | <math>\log_9{\displaystyle \frac{1}{3}}</math>
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|c)
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|width="33%" | <math>\log_2{0\textrm{.}125}</math>
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|-
 +
|d)
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|width="33%" | <math>\log_3{\left(9\cdot3^{1/3}\right)}</math>
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|e)
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|width="33%" | <math>2^{\log_{\scriptstyle2}{4}}</math>
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|f)
 +
|width="33%" | <math>\log_2{4}+\log_2{\displaystyle \frac{1}{16}}</math>
 +
|-
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|g)
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|width="33%" | <math>\log_3{12}-\log_3{4}</math>
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|h)
 +
|width="33%" | <math>\log_a{\bigl(a^2\sqrt{a}\,\bigr)}</math>
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|}
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</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}}
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===Exercise 3.3:4===
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<div class="ovning">
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Simplify
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{| width="100%" cellspacing="10px"
 +
|a)
 +
|width="33%" | <math>\lg{50}-\lg{5}</math>
 +
|b)
 +
|width="33%" | <math>\lg{23}+\lg{\displaystyle \frac{1}{23}}</math>
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|c)
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|width="33%" | <math>\lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}</math>
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|}
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</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}}
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===Exercise 3.3:5===
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<div class="ovning">
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Simplify
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{| width="100%" cellspacing="10px"
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|a)
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|width="33%" | <math>\ln{e^3}+\ln{e^2}</math>
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|b)
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|width="33%" | <math>\ln{8}-\ln{4}-\ln{2}</math>
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|c)
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|width="33%" | <math>(\ln{1})\cdot e^2</math>
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|-
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|d)
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|width="33%" | <math>\ln{e}-1</math>
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|e)
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|width="33%" | <math>\ln{\displaystyle \frac{1}{e^2}}</math>
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|f)
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|width="33%" | <math>\left(e^{\ln{e}}\right)^2</math>
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|}
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</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}}
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 +
===Exercise 3.3:6===
 +
<div class="ovning">
 +
{| width="100%"
 +
| 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''.
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{| width="100%" cellspacing="10px"
 +
|a)
 +
|width="100%" | <math>\log_3{4}</math>
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|-
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|b)
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|width="100%" | <math>\lg{46}</math>
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|-
 +
|c)
 +
|width="100%" | <math>\log_3{\log_2{(3^{118})}}</math>
 +
|}
 +
||{{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) log39313  e) 2log24 f) log24+log2116
g) log312−log34 h) logaa2a 

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

Exercise 3.3:4

Simplify

a) lg50−lg5 b) lg23+lg123 c) lg2713+2lg3+lg91

Answer | Solution a | Solution b | Solution c

Exercise 3.3:5

Simplify

a) lne3+lne2 b) ln8−ln4−ln2 c) (ln1)e2
d) lne−1 e) ln1e2 f) elne2 

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





Answer | Solution a | Solution b | Solution c

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