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3.3 Exercises

From Förberedande kurs i matematik 1

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       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) \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)}

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

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}}

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

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) \displaystyle \log_3{4}
b) \displaystyle \lg{46}
c) \displaystyle \log_3{\log_2{(3^{118})}}





Answer | Solution a | Solution b | Solution c

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