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