$\displaystyle 3\ln2<2\ln(x)<2\ln3$
Express the solution x as a set using the notations ()[]
Can anyone help me out?
EDIT: Please don't skip any steps that may seem arbitrary to you =] thanks again
$\displaystyle 3\ln2<2\ln(x)<2\ln3$
Express the solution x as a set using the notations ()[]
Can anyone help me out?
EDIT: Please don't skip any steps that may seem arbitrary to you =] thanks again
We begin:
$\displaystyle 3 \ln 2 < 2 \ln 2x < 2 \ln 3$
$\displaystyle (3/2) \ln 2 < \ln 2x < \ln 3$
$\displaystyle \ln (2^{3/2}) < \ln 2x < \ln 3$
Since the natural logarithm is an increasing function, we have:
$\displaystyle 2^{3/2} < 2x < 3$
$\displaystyle 2\sqrt{2} < 2x < 3$
$\displaystyle \sqrt{2} < x < 3/2$