Calculate the expression with logarithm Show that 
$$1-\frac{2}{3}^{\frac{1}{\log_2{\frac{2}{3}}}}=\frac{1}{2}.$$
I was trying to calculate it but I failed anytime. 
I would be grateful for help.

Since $x^{\frac{1}{\log_2 x}} =  x^{\log_x 2} = 2$ then for $x = \frac{2}{3}$ we get
$$(\frac{2}{3})^{\frac{1}{\log_2 \frac{2}{3}}} = 2$$
So
$$1 - (\frac{2}{3})^{\frac{1}{\log_2 \frac{2}{3}}}  = -1$$
