Solution:

$log\big(\frac{2}{3}\big) + log\big(\frac{4}{5}\big) - log\big(\frac{8}{15}\big) = log\big(\frac{2}{5} x \frac{4}{5}\big) - log\big(\frac{8}{15}\big)$

$= log\big(\frac{8}{15}\big)- log\big(\frac{8}{15}\big)$

$= 0 OR log\Bigg(\frac{\frac{8}{15}}{\frac{8}{15}}\Bigg)$

$= log(1) = 0$