対数法則により
与式 = log_(\(\frac{1}{2}\)) (\(\frac{8}{13}\)) - log_(\(\frac{1}{2}\)) (\(\frac{2}{3}\)\()^{2}\) + log_(\(\frac{1}{2}\)) (\(\frac{26}{9}\))
= log_(\(\frac{1}{2}\)) ((8×9×26)/(13×4×9))
= log_(\(\frac{1}{2}\)) 4 = (lo\(g_{2}\) 4)/(lo\(g_{2}\) (\(\frac{1}{2}\))) [底の変換公式]
= 2/(-1) = -2.