S1 2013 vår LØSNING

Oppgave 1

a)

$2lgx + 3 = 5 \\ 2lgx =2 \\ lg x=1 \\ 10^{lgx} 10^1 \\x=10$

b)

$2x^2+2x=12\\ 2x^2+2x-12=0 \\ x= \frac{-2\pm \sqrt{4+4 \cdot 2 \cdot 12}}{4} \\ x= \frac{-2 \pm 10}{4} \\ x= -3 \vee x= 2$

Oppgave 3

a)

$ \frac{2^{-3} \cdot a^0 \cdot (a \cdot b)^2}{2^{-4} \cdot a^{-1} \cdot b^2}= \frac{2^4a^3b^2}{2^3b^2} = 2a^3$

b)

$lg(ab) ^2- lg ( \frac{a^3}{b^2}) + lg(ab^2)= \\ 2(lga +lgb) - ( lg a^3 - lg b^2 ) + lga + lg b^2 = \\ 2lga+ 2lgb -3lga + 2lgb +lga + 2lgb = \\ 6 lgb$

Oppgave 5

a)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1