The solution of the equation |x-1|^ _3 x^2-2 _8 9 =(x-1)^7 is/are

The solution of the equation

|x-1|^{\log _3 x^2-2 \log _8 9}=(x-1)^7

is/are

Options

A $2$
B $81$
C $\frac{1}{\sqrt{3}}$
D $3$

Correct answer

B. $81$

Step-by-step solution

\because x-1\gt0

Taking log both sides \left(\log _3 x^2-2 \log _x 9\right) \log (x-1)=7 \log (x-1)\Rightarrow x=81, \frac{1}{\sqrt{3}}, 2\therefore x \neq \frac{1}{\sqrt{3}}\therefore x=2,81

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