Answer:
A = 6
B = 3
C = 9
Step-by-step explanation:
We start by using repeatedly the product rule of logarithms that converts the logarithm of a product of two factors into the addition of logarithms: [tex]log (A*B)=log(A) + log(B)[/tex]:
[tex]log (x^6*y^3*z^9)= log (x^6*[y^3*z^9])=log(x^6)+log(y^3*z^9)=\\=log(x^6)+log(y^3)+log(z^9)[/tex]
At this point we use on each term of the expression we found above, the power rule of logarithms that states: [tex]log(A^m)=m*log(A)[/tex]
This gives as:
[tex]log(x^6)+log(y^3)+log(z^9)=6*log(x)+3*log(y)+9*log(z)[/tex]
Therefore, the coefficients A, B, and C requested are:
A = 6
B = 3
C = 9
