Помогите решить чот не вдупляю. Created by qwe892137. algebra-ru

Помогите решить чот не вдупляю...

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${3}^{ \frac{ log_{3}(5) }{ log_{5}(3) } } - {5}^{ log_{3}(5) } + {7}^{ log_{7}(49) } = { ({3}^{ log_{3}(5) } )}^{ \frac{1}{ log_{5}(3) } } - {5}^{ log_{3}(5) } + {7}^{ log_{7}(49) } = \\ \\ = {5}^{ log_{3}(5) } - {5}^{ log_{3}(5) } + 49 = 49 \\ \\$

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${a}^{log_{a}(b)} = b \\ \\ \frac{1}{ log_{a}(b) } = log_{b}(a) \\$

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ОТВЕТ: 49

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NNNLLL54

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$3^{\frac{log_35}{log_53}}-5^{log_35}+7^{log_749}=\Big [\; a^{log_{a}b}=b\; \Big ]=3^{log_35\cdot \frac{1}{log_53} }-5^{log_35}+49=\\\\=\Big [\; \frac{1}{log_{a}b}=log_{b}a\; \Big ]=3^{log_35\cdot log_35}-5^{log_35}+49=\\\\=(3^{log_35})^{log_35}-5^{log_35}+49=5^{log_35}-5^{log_35}+49=49$

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