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3.3 Übungen

Aus Online Mathematik Brückenkurs 1

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Version vom 14:07, 3. Aug. 2008

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Exercise 3.3:1

What is \displaystyle \,x\, if

a)	\displaystyle 10^x=1\,000	b)	\displaystyle 10^x=0{,}1
c)	\displaystyle \displaystyle \frac{1}{10^x}=100	d)	\displaystyle \displaystyle \frac{1}{10^x}=0{,}000\,1

Svar

Lösning a

Lösning b

Lösning c

Lösning d

Exercise 3.3:2

Calculate

a)	\displaystyle \lg{ 0{,}1}	b)	\displaystyle \lg{ 10\,000}	c)	\displaystyle \lg {0{,}001}	d)	\displaystyle \lg {1}
e)	\displaystyle 10^{\lg{2}}	f)	\displaystyle \lg{10^3}	g)	\displaystyle 10^{-\lg{0{,}1}}	h)	\displaystyle \lg{\displaystyle \frac{1}{10^2}}

Svar

Lösning a

Lösning b

Lösning c

Lösning d

Lösning e

Lösning f

Lösning g

Lösning h

Exercise 3.3:3

Calculate

a)	\displaystyle \log_2{8}	b)	\displaystyle \log_9{\displaystyle \frac{1}{3}}	c)	\displaystyle \log_2{0{,}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)}

Svar

Lösning a

Lösning b

Lösning c

Lösning d

Lösning e

Lösning f

Lösning g

Lösning h

Exercise 3.3:4

Simplify

\displaystyle \lg{50}-\lg{5}

\displaystyle \lg{23}+\lg{\displaystyle \frac{1}{23}}

\displaystyle \lg{27^{1/3}}+\displaystyle \frac{\lg{3}}{2}+\lg{\displaystyle \frac{1}{9}}

Svar

Lösning a

Lösning b

Lösning 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