Question 193720
*[Tex \LARGE \log_{a}\left(\frac{x^3}{yz^{16}}\right)] ... Start with the given expression



*[Tex \LARGE \log_{a}\left(x^3\right)-\log_{a}\left(yz^{16}\right)] ... Expand the log using the identity {{{log(b,(x/y))=log(b,(x))-log(b,(y))}}}



*[Tex \LARGE \log_{a}\left(x^3\right)-\left\[\log_{a}\left(y\right)+\log_{a}\left(z^{16}\right)\right\]] ...  ... Expand the second log using the identity {{{log(b,(x*y))=log(b,(x))+log(b,(y))}}}



*[Tex \LARGE \log_{a}\left(x^3\right)-\log_{a}\left(y\right)-\log_{a}\left(z^{16}\right)] ... Distribute



*[Tex \LARGE 3\log_{a}\left(x\right)-\log_{a}\left(y\right)-16\log_{a}\left(z\right)] ... Pull down the exponents using the identity {{{log(b,(x^y))=y*log(b,(x))}}}.



So *[Tex \LARGE \log_{a}\left(\frac{x^3}{yz^{16}}\right)=3\log_{a}\left(x\right)-\log_{a}\left(y\right)-16\log_{a}\left(z\right)]



So A=3, B=-1 and C=-16