1 step. Note that
[tex]x>0,\\ \\x-3>0\Rightarrow x>3.[/tex]
Therefore, possible x are [tex]x>3.[/tex]
2 step. Use property [tex]\log_ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]
Then
[tex]\log_{81}32x-\log_{81}(x-3)=\log_{81}\dfrac{32x}{x-3}.[/tex]
3 step.
[tex]\log_{81}\dfrac{32x}{x-3}=\dfrac{3}{4}\Rightarrow 81^{\log_{81}\frac{32x}{x-3}}=81^{\frac{3}{4}},\\ \\\dfrac{32x}{x-3}=(3^4)^{\frac{3}{4}},\\ \\\dfrac{32x}{x-3}=27,\\ \\32x=27(x-3),\\ \\32x=27x-81,\\ \\5x=-81,\\ \\x=-\dfrac{81}{5}.[/tex]
4 step. Since [tex]-\dfrac{81}{5}<3,[/tex] this solution is extra.
Answer: no solution, choice D.
