Bring up the coefficients as exponents:
[tex]\log _62^3+\log _63^2-\log _6x=2[/tex]Apply product rule of log and quotient rule:
[tex]\log _6((2^3\times3^2)/x)=2[/tex][tex]\log _{6\text{ }}((8\times9)/x)=2[/tex][tex]\log _{6\text{ }}\frac{72}{x}=2[/tex]If log6 (72/x) = 2, then 72/x= 6^2
[tex]72/x=6^2[/tex][tex]72/x=36[/tex][tex]72/36\text{ = x}[/tex][tex]x=2[/tex]