3 ln 2 - 3 ln x - 1/2 ln x = -1

3 ln 2 + 1 = 3 ln x + 1/2 ln x ( Moving the terms )

3 ln 2 + 1 = ln x^3 + ln x^1/2

3 ln 2 + 1 = ln (x^3 * x^1/2)

3 ln 2 + 1 = ln (x^3.5) ( Rule of indices Take note 3.5 = 7/2 )

3 ln 2 + 1 = 7/2 ln x

2/7 (3 ln 2+1) = ln x

ln x = 2/7 (3 ln 2+1)

Hope it helps. To understand logarithm better visit the site listed below :

http://www.intmath.com/Exponential-l...rithm-laws.php