Question

Log 25/5 na base 1/5
Log raíz de 27 na base 3

Answer 1

$\\ \\ \log_3(\sqrt{27})=\log_3(\sqrt{3^3})=\log_3(3^{\frac32})=\frac32\cdot\log_3(3)=\frac32$$\log_{\frac15}(\frac{25}{5})=\log_{\frac15}(5)=\log_{\frac15}(\frac15)^{-1}=-1\cdot\log_{\frac15}(\frac15)=-1$

Answer 2

$a) log_{ \frac{1}{5} } \frac{25}{5} = log_{ \frac{1}{5} } 5 \\ \\ log_{ \frac{1}{5} } 5 = x \\ \\ ( \frac{1}{5} )^{x}=5 \\ \\ 5^{-x}= 5 \\ \\ x = -1 \\ \\ b) log_{3} \sqrt{27} = log_{3} \sqrt{3^{3}} \\ \\ log_{3} 3^{ \frac{3}{2} }=x \\ \\ 3^{x}=3^{ \frac{3}{2} } \\ \\ x = \frac{3}{2}$

Espero ter ajudado.