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![\log_35\times\log_427\times\log_{25} \sqrt[3]{2} \\ \\ colocar~~na~~base~~10 \\ \\ \frac{log5}{log3} \times \frac{log27}{log4} \times \frac{log \sqrt[3]{2} }{log25} = \\ \\ \frac{log5}{log3} \times \frac{log3^3}{log2^2} \times \frac{log2^{ \frac{1}{3}} }{log5^2} = \\ \\ \frac{log5}{log3} \times \frac{3log3}{2log2} \times \frac{1/3log2}{2log5} \\ \\ cancelar~~os~~iguais \\ \\ \frac{3\times1/3}{2\times2} = \frac{1}{4}](https://tex.z-dn.net/?f=%5Clog_35%5Ctimes%5Clog_427%5Ctimes%5Clog_%7B25%7D+%5Csqrt%5B3%5D%7B2%7D++%5C%5C++%5C%5C+colocar%7E%7Ena%7E%7Ebase%7E%7E10+%5C%5C++%5C%5C++%5Cfrac%7Blog5%7D%7Blog3%7D+%5Ctimes+%5Cfrac%7Blog27%7D%7Blog4%7D+%5Ctimes+%5Cfrac%7Blog+%5Csqrt%5B3%5D%7B2%7D+%7D%7Blog25%7D+%3D+%5C%5C++%5C%5C++%5Cfrac%7Blog5%7D%7Blog3%7D+%5Ctimes+%5Cfrac%7Blog3%5E3%7D%7Blog2%5E2%7D+%5Ctimes++%5Cfrac%7Blog2%5E%7B+%5Cfrac%7B1%7D%7B3%7D%7D+%7D%7Blog5%5E2%7D++%3D+%5C%5C++%5C%5C++%5Cfrac%7Blog5%7D%7Blog3%7D+%5Ctimes+%5Cfrac%7B3log3%7D%7B2log2%7D+%5Ctimes+%5Cfrac%7B1%2F3log2%7D%7B2log5%7D++%5C%5C++%5C%5C+cancelar%7E%7Eos%7E%7Eiguais+%5C%5C++%5C%5C++%5Cfrac%7B3%5Ctimes1%2F3%7D%7B2%5Ctimes2%7D+%3D+%5Cfrac%7B1%7D%7B4%7D+ "\log_35\times\log_427\times\log_{25} \sqrt[3]{2} \\ \\ colocar~~na~~base~~10 \\ \\ \frac{log5}{log3} \times \frac{log27}{log4} \times \frac{log \sqrt[3]{2} }{log25} = \\ \\ \frac{log5}{log3} \times \frac{log3^3}{log2^2} \times \frac{log2^{ \frac{1}{3}} }{log5^2} = \\ \\ \frac{log5}{log3} \times \frac{3log3}{2log2} \times \frac{1/3log2}{2log5} \\ \\ cancelar~~os~~iguais \\ \\ \frac{3\times1/3}{2\times2} = \frac{1}{4}")
leliswoodovcgwa:
Muito bom Katy, a resposta que estávamos chegando era muito mirabolante, um cálculo imenso e sem nexo, um deles o resultado era até o mesmo, mas não acabava, muito obrigado mesmo
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