SOLUTION: if log{a}((x^3)/(y{z}^16))=Alog{a}(x)+Blog{a}(y)+Clog{a^2}
A=? B=? C=?
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Question 193720: if log{a}((x^3)/(y{z}^16))=Alog{a}(x)+Blog{a}(y)+Clog{a^2}
A=? B=? C=?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
)
... Start with the given expression
-\log_{a}\left(yz^{16}\right))
... Expand the log using the identity
-\left\[\log_{a}\left(y\right)+\log_{a}\left(z^{16}\right)\right\])
... ... Expand the second log using the identity
-\log_{a}\left(y\right)-\log_{a}\left(z^{16}\right))
... Distribute
-\log_{a}\left(y\right)-16\log_{a}\left(z\right))
... Pull down the exponents using the identity .
So =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
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