<div class="clay6-step-odd"><div class="clay6-basic" id="pr10">$\int \log _a x dx$</div><div class="clay6-basic" id="pr11">=> $\int \large\frac{\log _e x }{\log _e a }$$dx$</div><div class="clay6-basic" id="pr12">=> $ \large\frac{1}{\log _e a }$$\int \log _e x dx$</div><div class="clay6-basic" id="pr13">=> $\large\frac{1}{\log _e a} $$\bigg\{ \log _e x.x -\int \large\frac{1}{x}.$$xdx \bigg \}$</div><div class="clay6-basic" id="pr14">=> $\large\frac{1}{\log a} $$\{ x \log _e x -x \}+c$</div><div class="clay6-basic" id="pr15">$\large\frac{x}{\log a } $$(\log x -1)+c$</div><div class="clay6-basic" id="pr16">Hence a is the correct answer. </div></div>