Question

\(\left(\dfrac{32}{243}\right)^x=\left(\dfrac{3}{2}\right)^{-1}\)

Answer 1

Giải:

\(\left(\dfrac{32}{243}\right)^x=\left(\dfrac{3}{2}\right)^{-1.}\)

\(\Leftrightarrow\left(\dfrac{2^5}{3^5}\right)^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left[\left(\dfrac{2}{3}\right)^5\right]^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{2}{3}\right)^4.\)

\(\Rightarrow5x=4\Rightarrow x=\dfrac{4}{5}.\)

Vậy.....