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3.3 Exercises

From Förberedande kurs i matematik 1

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m (decimal comma --> decimal point)
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|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>
+
|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: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{,}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>
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|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>
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|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)

Revision as of 11:57, 19 August 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) \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)}

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

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})}}