Question

Log2/3 243/32=
Me ajudem!!!

Answer 1

$\log_{\tfrac{2}{3}}\left(\frac{243}{32} \right )=x \Rightarrow \left(\frac{2}{3} \right )^{x}=\frac{243}{32}\\ \\ \left(\frac{2}{3} \right )^{x}=\frac{3^{5}}{2^{5}}\\ \\ \left(\frac{2}{3} \right )^{x}=\left(\frac{3}{2} \right )^{5}\\ \\ \left(\frac{2}{3} \right )^{x}=\left[\left(\frac{2}{3} \right )^{-1} \right ]^{5}\\ \\ \left(\frac{2}{3} \right )^{x}=\left(\frac{2}{3} \right )^{-5}\\ \\ x=-5 \Rightarrow \boxed{\log_{\tfrac{2}{3}}\left(\frac{243}{32} \right )=-5}$