Question

log de 625 de base 5√5

Answer 1

log     625
     5√5
==========================
  x   x              3
5 √5    =   5 . 5
=========cancelo os 5 x======
 x + 0,5x          3
5          =  5
==========================
3/2x = 3
x = 3/ (3/2)
x = 8/3

Answer 2

$\log_{5\sqrt5}625=x\Longleftrightarrow(5\sqrt{5})^x=625\\\\\\(5\sqrt{5})^x=5^4\\\\(5\cdot5^{\frac{1}{2}})^x=5^4\\\\(5^{1+\frac{1}{2}})^x=5^4\\\\(5^{\frac{3}{2}})^x=5^4\\\\5^{\frac{3x}{2}}=5^4\quad\\\\\therefore\\\\\quad\dfrac{3x}{2}=4\\\\3x=8\\\\x=\dfrac{8}{3}\\\\\\\\\boxed{\boxed{\log_{5\sqrt5}625=\dfrac{8}{3}}}$