Question 175448
Your representations of the problems are very difficult to decipher.  I think for the first one you mean:


{{{ln((((x + 8)(x - 9))/(x - 4)^4)^(3/2))}}}, {{{x > 9}}}


In which case,


Use the following rules:


{{{log(b,(x^n))=n*log(b,(x))}}}


The log of the product is the sum of the logs:  {{{log(b,(xy))=log(b,(x)) + log(b,(y))}}}


The log of the quotient is the difference of the logs:  {{{log(b,(x/y))=log(b,(x)) - log(b,(y))}}}



{{{ln((((x + 8)(x - 9))/(x - 4)^4)^(3/2))}}} → {{{(3/2)ln(((x + 8)(x - 9))/(x - 4)^4)}}} → {{{(3/2)(ln(x+8)+ln(x-9)-ln((x-4)^4))}}} →  {{{(3/2)(ln(x+8)+ln(x-9)-4*ln(x-4))}}} →  {{{(3/2)ln(x+8)+(3/2)ln(x-9)-6*ln(x-4)}}} →


Answer A.



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