Question

como resolver: log de 8 na base 0,25 ?

 

Answer 1

0,25 → 1/4 

$\log~8 =~x\\~~~~~~~ \frac{1}{4}$

$( \frac{1}{4})^x=8\\( \frac{1}{2^2} )^x=2^3\\(2^{-2})^x=2^3\\2^{-2x}=2^3$

$-2x=3$

$\boxed{x=- \frac{3}{2} }$

Answer 2

$\log_{0,25}8=x\\\\(0,25)^x=8\\\\\left(\frac{25}{100}\right )^x=8\\\\\left(\frac{1}{4}\right)^x=8\\\\(2^{-2})^x=8\\\\2^{-2x}=2^3\\\\-2x=3\\\\\boxed{x=\frac{-3}{2}}$