Processing Math: Done

From Förberedande kurs i matematik 1

The left-hand side is "2 raised to something", and therefore a positive number regardless of whatever value the exponent has. We can therefore take the log of both sides,

ln2x2−2=ln1

and use the log law lnab=blna to get the exponent x2−2 as a factor on the left-hand side,

x2−2ln2=ln1.

Because e0=1, so ln1=0, giving

(x2−2)ln2=0.

This means that x must satisfy the second-degree equation

x2−2=0.

Taking the root gives x=−2  or x=2 .

Note: The exercise is taken from a Finnish upper-secondary final examination from March 2007.