Rewrite the following expression using the properties of logarithms. log2z+2log2x+4log9y+12log9x−2log2y

Use the rules of logarithm:
1. log(x)+log(y)=log(xy)
    log(x)-log(y)=log(x/y)
2. k*log(x) = log(x^k)
    log(x)/k = log(x^(1/k))

log(2z)+2log(2x)+4log(9y)+12log(9x)−2log(2y)
=log(2z)+log(4x^2)+log(9^4y^4)+log(9^12x^12)−log(4y^2)
=log(2z)+log(4x^2)+log(6561y^4)+log(282429536481x^12)−log(4y^2)
=log(59296646043258912 * x^14 * y^6 * z)

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Yes. there is a constant ratio of number of calories to gram of protein.12/3=24/4=32/8=44/11=4