apply the property of the potency for those that have coefficients
[tex]b\cdot\log x=\log (x^b)[/tex]apply the product property and the quotient product to leave it as a single log
[tex]\begin{gathered} \log (a)+\log (b)=\log (a\cdot b) \\ \log (a)-\log (b)=\log (\frac{a}{b}) \end{gathered}[/tex]simplify the expression using this properties
[tex]\begin{gathered} \log _2(z)+2\log _2(x)+4\log (y)+12\log (x)-2\log _2(y) \\ \log _2(z)+\log _2(x^2)+\log (y^4)+\log (x^{12})-\log _2(y^2) \\ \log _2(x^2z)+\log (x^{12}y^4)-\log _2(y^2)^{} \\ \log _2(\frac{x^2z}{y^2})+\log (x^{12}y^4) \end{gathered}[/tex]