Question

Log2 z + 2 log2 x + 4 log, y + 12 logg x - 2 log2 y

Answer 1

`\log _2(z)+2\log _2(x)+4\log (y)+12\log (x)-2\log _2(y)`

apply the property of the potency for those that have coefficients

`b\cdot\log x=\log (x^b)`

apply the product property and the quotient product to leave it as a single log

`\begin{gathered} \log (a)+\log (b)=\log (a\cdot b) \\ \log (a)-\log (b)=\log ((a)/(b)) \end{gathered}`

simplify the expression using this properties

`\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((x^2z)/(y^2))+\log (x^(12)y^4) \end{gathered}`