How do you condense 2(ln)X + 1/2(ln)Y?

May 8, 2016

$2 \ln X + \frac{1}{2} \ln Y = \ln {X}^{2} \cdot \sqrt{Y}$

Explanation:

$2 \ln X + \frac{1}{2} \ln Y$

= $\ln {X}^{2} + \ln {Y}^{\frac{1}{2}}$ (as $n \ln a = \ln {a}^{n}$)

= $\ln {X}^{2} \cdot {Y}^{\frac{1}{2}}$

= $\ln {X}^{2} \cdot \sqrt{Y}$