Question
Solve$ : (\sqrt{3})^{x-3}=(\sqrt[4]{3})^{x+1}$
✓
Answer
$ (\sqrt{3})^{x-3}=(\sqrt[4]{3})^{x+1}$
$ \Rightarrow\left(3^{\frac{1}{2}}\right)^{x-3}=\left(3^{\frac{1}{4}}\right)^{x+1}$
$ \Rightarrow 3^{\frac{x-3}{2}}=3^{\frac{x+1}{4}}$
$ \Rightarrow \frac{x-3}{2}=\frac{x+1}{4}$
$ \Rightarrow 4(x-3)=2(x+1)$
$ \Rightarrow 4 x-12=2 x+2$
$ \Rightarrow 4 x-2 x=12+2$
$ \Rightarrow 2 x=14$
$ \Rightarrow x=\frac{14}{2}$
$ \Rightarrow x=7$
$ \Rightarrow\left(3^{\frac{1}{2}}\right)^{x-3}=\left(3^{\frac{1}{4}}\right)^{x+1}$
$ \Rightarrow 3^{\frac{x-3}{2}}=3^{\frac{x+1}{4}}$
$ \Rightarrow \frac{x-3}{2}=\frac{x+1}{4}$
$ \Rightarrow 4(x-3)=2(x+1)$
$ \Rightarrow 4 x-12=2 x+2$
$ \Rightarrow 4 x-2 x=12+2$
$ \Rightarrow 2 x=14$
$ \Rightarrow x=\frac{14}{2}$
$ \Rightarrow x=7$
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