$$ \left(\frac25\right)\ln(1/2)+\left(\frac15\right)\ln(2) $$
Im having some difficulty with above quotient. Here is what i try to do.
$$ \left(\frac15\right)(2\ln(1/2)+\ln(2)) $$
$$ \left(\frac15\right)(\ln((1/2)^2)+\ln(2)) $$
$$ \left(\frac15\right)(\ln(1/4)+\ln(2)) $$
$$ \left(\frac15\right)(\ln(1)-\ln(4)+\ln(2)) $$
$$ \left(\frac15\right)(\ln(2)-(\ln(4)) $$
$$ \left(\frac15\right)(\ln(1/2)) $$
$$ \left(\frac15\right)(\ln(1)-\ln(2)) $$
Wolfram gets, but im not sure how $$ -3\log(2)/5 $$
You must have mistyped the question into wolfram. Wolfram gets the same answer as you do.