Lösung 3.4:3a
Aus Online Mathematik Brückenkurs 1
Both left- and right-hand sides are positive for all values of x and this means that we can take the logarithm of both sides and get a more manageable equation,
After a little rearranging, the equation becomes
We complete the square of the left-hand side,
and move the constant terms over to the right-hand side,
It can be difficult to see whether the right-hand side is positive or not, but if we remember that \displaystyle e > 2 and that thus \displaystyle \ln 2 < \ln e = 1\,, we must have that \displaystyle (1/\ln 2)^{2} > 1\,, i.e. the right-hand side is positive.
The equation therefore has the solutions
which can also be written as
