Mathematics - Area Under Curves Question with Solution | TestHub

Let $A=\left(p,{\log }_{a}p\right),B=\left(q,2{\log }_{a}q\right),C=\left(q,3{\log }_{a}q\right)$ with $p,q>0,a>0,a\ne 1.AB\Vert \mathrm{X}$-axis gives ${\log }_{a}p=2{\log }_{a}q$, so $p=q^2$. The side length is $6:|BC|=\left|{\log }_{a}q\right|=6$ and $|AB|=|p-q|=6$. Taking $q=a^6$, $p=a^{12}:a^{12}-a^6=6\Rightarrow {\left(a^6\right)}^2-a^6-6=0\Rightarrow a^6=3$, so $a=3^{1/6}$.