we have the system of equations
[tex]\begin{gathered} f(x)=\log_2x+2 \\ g(x)=\log_2x^3-6 \end{gathered}[/tex]
Equate the functions f(x) and g(x)
[tex]\log_2x+2=\log_2x^3-6[/tex]
Apply property of logarithms
[tex]\begin{gathered} \operatorname{\log}_2x+2=3\operatorname{\log}_2x-6 \\ 3\operatorname{\log}_2x-\operatorname{\log}_2x=2+6 \\ 2\operatorname{\log}_2x=8 \\ \operatorname{\log}_2x=4 \end{gathered}[/tex]
Apply the definition of logarithm
[tex]\begin{gathered} 2^4=x \\ x=16 \end{gathered}[/tex]
