Question 1164820
given:

{{{ln((x^15(x-1)^(1/2))/(3x-16))=A*ln(x)+B*ln(x-1)+C*ln(3x-16)}}}


{{{ln((x^15(x-1)^(1/2))/(3x-16))}}}


={{{ln(x^15(x-1)^(1/2))-ln(3x-16)}}}


={{{ln(x^15)+ln((x-1)^(1/2))-ln(3x-16)}}}


={{{15ln(x)+(1/2)ln(x-1)-ln(3x-16)}}}

so, {{{A=15}}}, {{{B=1/2}}}, and {{{C=1}}}


and

{{{ln((x^15(x-1)^(1/2))/(3x-16))=15*ln(x)+(1/2)*ln(x-1)-ln(3x-16)}}}