Question

Calcule log de 4 na base 1/4 + log de 1/4 na base 4?

Answer 1

$\large\begin{array}{l}\ell og_{\frac{1}{4}}(4)+\ell og_4(\frac{1}{4})\\\\\ell og_{4^{-1}}(4)+\ell og_4(4^{-1})\\\\-\ell og_4(4)+\begin{pmatrix}-\ell og_4(4)\end{pmatrix}\\\\-1+(-1)\\\\-1-1\\\\\fbox{ -2 }\end{array}$

Answer 2

Log(1/4) 4 + Log(4) 1/4
Log(1/4) 4=x. Log(4) 1/4=y
1/4^x=4. 4^y= 1/4
4^-x=4. 4^y= 4^-1
x=-1. y=-1

logo
-1+(-1)=-2