Question
Solve : $\left[3^x\right]^2: 3 \mathrm{x}=9: 1$
✓
Answer
$ {\left[3^x\right]^2: 3 x=9: 1}$
$ \Rightarrow \frac{\left[3^x\right]^2}{3^x}=\frac{9}{1}$
$ \Rightarrow\left[3^x\right]^2=9 \times 3^x$
$ \Rightarrow\left[3^x\right]^2=3^2 \times 3^x$
$ \Rightarrow\left[3^x\right]^2=3^{x+2}$
We know that if bases are equal, the powers are equal.
$\Rightarrow x^2=x+2$
$ \Rightarrow x^2-x-2=0$
$ \Rightarrow x^2-2 x+x-2=0$
$ \Rightarrow x(x-2)+1(x-2)=0$
$ \Rightarrow(x+1)(x-2)=0$
$ \Rightarrow x+1=0$ or $x-2=0$
$ \Rightarrow x=-1$ or $x=2$
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