MELBOURNE, Sept 15 (Reuters) - London copper fell to a three-month low Monday after data showed that China's industrial growth in August fell to a six-year low, triggering worries about its metal demand. But the Shanghai copper to find support, traders bet on China's central bank will inject new liquidity to support the economy, against the real estate-led economic downturn. On the London Metal Exchange (LME), copper for the three-month period dipped 0.6 percent to $ 6,798 a tonne, closing the previous session.