`(log_a a²b.log_a ab -2)/(log_a b)=5`

`<=>(log_a a²+log_a b)(log_a a+log_a b)-2=5log_a b`

`<=>(2+log_a b)(1+log_a b)-2-5log_a b=0`

`<=>log²_a b+3log_ab+2-2-5log_a b=0`

`<=>log²_a b-2log_a b=0`

`<=>log_a b(log_a b-2)=0`

`<=>` \(\left[ \begin{array}{l}log_a b=0(l) do:a,b\ne1\\log_a b=2\end{array} \right.\) 

`=>log_a b=2`

`=>log_b a=1/2`