9|3x-1|=3to power8x-2

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{I} \mathrm{assume} \mathrm{your} \mathrm{question} \mathrm{is} \\ {9}^{\left|3\mathrm{x}-1\right|}=3^{8\mathrm{x}-2} \\ \Rightarrow {3^2}^{\left|3\mathrm{x}-1\right|}=3^{8\mathrm{x}-2} \\ \Rightarrow 2\left|3\mathrm{x}-1\right|=8\mathrm{x}-2=2\left(4\mathrm{x}-1\right) \\ \Rightarrow \left|3\mathrm{x}-1\right|=4\mathrm{x}-1...\left(\mathrm{i}\right) \\ \Rightarrow 3\mathrm{x}-1=4\mathrm{x}-1 \mathrm{or} 3\mathrm{x}-1=-\left(4\mathrm{x}-1\right) \\ \Rightarrow 3\mathrm{x}=4\mathrm{x} \mathrm{or} 3\mathrm{x}-1=-4\mathrm{x}+1 \\ \Rightarrow 4\mathrm{x}-3\mathrm{x}=0 \mathrm{or} 3\mathrm{x}+4\mathrm{x}=2 \\ \Rightarrow \mathrm{x}=0 \mathrm{or} \mathrm{x}=\frac{2}{7} \\ \mathrm{But} \mathrm{x}=0 \mathrm{does} \mathrm{not} \mathrm{satisfy} \left(\mathrm{i}\right) \\ \mathrm{Hence} \\ \mathrm{x}=\frac{2}{7} \left[\mathrm{Answer}\right] \end{gathered}$$

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