Question

Como faze esse log ?

Answer 1

Boa noite!

c)
$x=5^{\log_{25} 2}\\\log_5 x=\log_{25} 2\\\log_5 x=\dfrac{\log_5 2}{\log_5 25}\\\log_5 x=\dfrac{\log_5 2}{\log_5 5^2}\\\log_5 x=\dfrac{\log_5 2}{2}\\2\log_5 x=\log_5 2\\\log_5 x^2=\log_5 2\\x^2=2\\x=\sqrt{2}$

d)
$y=8^{\log_4 5}\\\log_8 y=\log_4 5\\\dfrac{\log_2 y}{\log_2 8}=\dfrac{\log_2 5}{\log_2 4}\\\dfrac{\log_2 y}{\log_2 2^3}=\dfrac{\log_2 5}{\log_2 2^2}\\\dfrac{\log_2 x}{3\log_2 2}=\dfrac{\log_2 5}{2\log_2 2}\\\dfrac{1}{3}\log_2 x=\dfrac{1}{2}\log_2 5\\\log_2 x^{1/3}=\log_2 5^{1/2}\\x^{1/3}=5^{1/2}\\x=5^{3/2}$

Uma forma rápida de se chegar nas mesmas respostas:
$\left(a^n\right)^{\log_{a^m} k}=k^{n/m}$

Espero ter ajudado!