Question

log de 5 raiz cubica de 25 na base 625

Answer 1

Yasmyn
Vamos passo a passo

               $log(625)5 \sqrt[3]{25} =x \\ \\ log(625)( \sqrt[3]{25})^5=x \\ \\ log(625)[(5^2) ^{ \frac{1}{3} }]^5 =x \\ \\ log(5^4) 5^{ \frac{10}{3} } =x \\ \\5 ^{ \frac{10}{3} }=[(5^4)}^x \\ \\ 5^{ \frac{10}{3} } = 5^{4x} \\ \\ \frac{10}{3}=4x \\ \\ 10=12x \\ \\ x= \frac{10}{12} \\ \\ x= \frac{5}{6}$

Answer 2

log 5 ∛25
   625
log  5 . 25 ¹/³
   625  

     x
625     = 5 . 25 ¹/³

       x                   4x            3(1/3)
(5⁴ )  = 125¹/³ = 5         = 5 

4 x = 3/3
4 x = 1
x = 1/4

log 5 ∛25  = 1/4
 625