# Thread: Help with an inequality.

1. ## Help with an inequality.

$3\ln2<2\ln(x)<2\ln3$

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

2. We begin:

$3 \ln 2 < 2 \ln 2x < 2 \ln 3$

$(3/2) \ln 2 < \ln 2x < \ln 3$

$\ln (2^{3/2}) < \ln 2x < \ln 3$

Since the natural logarithm is an increasing function, we have:

$2^{3/2} < 2x < 3$

$2\sqrt{2} < 2x < 3$

$\sqrt{2} < x < 3/2$