Solution 3.4:2a
From Förberedande kurs i matematik 1
The left-hand side is "
and use the log law \displaystyle \lg a^{b}=b\centerdot \lg a to get the exponent \displaystyle x^{\text{2}}-\text{2 } as a factor on the left-hand side
\displaystyle \left( x^{\text{2}}-\text{2 } \right)\ln 2=\ln 1
Because
\displaystyle e^{0}=1, so
\displaystyle \text{ln 1}=0, giving:
\displaystyle \left( x^{\text{2}}-\text{2 } \right)\ln 2=0
This means that
\displaystyle x
must satisfy the second-degree equation
\displaystyle \left( x^{\text{2}}-\text{2 } \right)=0
Taking the root gives
\displaystyle x=-\sqrt{2}
or
\displaystyle x=\sqrt{2}.
NOTE: the exercise is taken from a Finnish upper-secondary final examination from March 2007.
