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[tex] log_{3}8* log_{2}27- 3^{ log_{9}5 }= [/tex]

Răspuns :


[tex]log_3 8\cdot log_2 27-3^{log_9 5}=log_3 2^3\cdot log_2 3^3-3^{log_{3^2}5}=\\\\=3\cdot log_3 2\cdot 3\cdot log_2 3-3^{\dfrac{1}{log_5 3^2}}=9\cdot log_3 2\cdot\dfrac{1}{log_3 2}-3^{\dfrac{1}{2}\cdot\dfrac{1}{log_5 3}}=\\\\=9-\left(3^{log_3 5}\right)^{\frac{1}{2}}=9-\sqrt5.[/tex]

Green eyes.