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take on 〜と対戦［対決］する、〜と争う、〜と戦う、〜に挑戦する、〜を相手に取り組む、〜を相手にする

They decided to take on the authorities. 彼らは当局と対決することを決めた

He stole the limelight from the DPJ by recruiting a team of high-profile candidates, many of them new to politics (and dubbed “assassins” by Japan's media), to take on the LDP rebels in their home districts.

hammer away せっせと働く、（問題に）取り組む、しつこく働きかける、説得する、たたき続ける、繰り返して言う、強調する

hammer away at mathematics 数学をコツコツ勉強する

While Mr Koizumi is perched on high, hammering away at one issue like a woodpecker and dazzling the media with his plumage, the DPJ is waving a giant axe at the base of the tree, frantically trying to attract voters' attention.