Combine the left hand side, then write both sides as powers of 6:
[tex]\log_64x^2-\log_6x=\log_6\dfrac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2[/tex]
[tex]\implies\dfrac{4x^2}x=36[/tex]
[tex]\implies x^2=9x[/tex]
[tex]\implies x^2-9x=x(x-9)=0[/tex]
[tex]\implies x=0,x=9[/tex]
However, for any base [tex]b[/tex], [tex]\log_bx[/tex] is undefined if [tex]x=0[/tex], so the only solution is [tex]x=9[/tex].
