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

Warning: jsMath requires JavaScript to process the mathematics on this page.
If your browser supports JavaScript, be sure it is enabled.

3.3 Exercises

From Förberedande kurs i matematik 1

(Difference between revisions)

Jump to: navigation, search

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

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

\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}}

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

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})}}