Question

(3/2)^x+2=81/16

2x^2-5x=1

Answer 1

\(\left(\dfrac{3}{2}\right)^{x+2}=\dfrac{81}{16}\)

\(\left(\dfrac{3}{2}\right)^x.\left(\dfrac{3}{2}\right)^2=\dfrac{81}{16}\)

\(\left(\dfrac{3}{2}\right)^x=\dfrac{81}{16}:\dfrac{9}{4}=\dfrac{9}{4}\)

\(\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^2\)

⇔\(x=2\)

 

Answer 2

a: Ta có: \(\left(\dfrac{3}{2}\right)^{x+2}=\dfrac{81}{16}\)

\(\Leftrightarrow x+2=4\)

hay x=2

b: Ta có: \(2^{x^2-5x}=1\)

\(\Leftrightarrow x\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)