Question

- calcule o logaritmo de 625 na base 5 ³√5?

Answer 1

$\log_{5^3 \sqrt{5} } 625 =x \Rightarrow (5^3 \sqrt{5} )^x=625\\\\(5^3.5^ \frac{1}{2} ) ^ x =5^4 \Rightarrow (5^{3+ \frac{1}{2} })^{x} = 5^4 \Rightarrow \dfrac{7}{2} x=4 \Rightarrow \Larged\boxed{x= \dfrac{8}{7} }$