Question

Calcule o produto de:

Log₃⁵ . log₄²⁷ . log₂₅$\sqrt[3]{2}$

Answer 1

vamos lá...

$\log_35\times\log_427\times\log_{25} \sqrt[3]{2} \\ \\ colocar~~na~~base~~10 \\ \\ \frac{log5}{log3} \times \frac{log27}{log4} \times \frac{log \sqrt[3]{2} }{log25} = \\ \\ \frac{log5}{log3} \times \frac{log3^3}{log2^2} \times \frac{log2^{ \frac{1}{3}} }{log5^2} = \\ \\ \frac{log5}{log3} \times \frac{3log3}{2log2} \times \frac{1/3log2}{2log5} \\ \\ cancelar~~os~~iguais \\ \\ \frac{3\times1/3}{2\times2} = \frac{1}{4}$