Question

81/16×(3/2)^x=(-3/2)^20

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Answer 1

\(\Leftrightarrow\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^{20}:\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^{16}\)

=>x=16

Answer 2

\(\dfrac{81}{16}\cdot\left(\dfrac{3}{2}\right)^x=\left(-\dfrac{3}{2}\right)^{20}\)

\(\left(\dfrac{3}{2}\right)^4\cdot\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^{20}\)

\(\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^{20}:\left(\dfrac{3}{2}\right)^4\)

\(\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^{\left(20-4=16\right)}\)

`=>x=16`