Practicing Success
Solve $x(2^x-1)(3^x -9)(x-3)<0$. |
$(2, 3)$ $(1, -1)$ $(0, -1)$ $(0, ∞)$ |
$(2, 3)$ |
Let $E = x(2^x-1)(3^x-9)(x-3)$ Here $2^x-1=0⇒x=0$ and when $3^x-9=0⇒x=2$ Now mark x = 0, 2 and 3 or real number line. The sign of E starts with a positive sign from right hand side. Also at x = 0, two factors vanish x and $2^x-1$; hence, the sign of E does not change wile crossing x = 0. The sign scheme of E is as follows: From the figure, we have E < 0 for $x ∈ (2, 3)$
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