Question

ln(x^3-5x^2+19)/ln(x-2)=3

Answer 1

\[\ln (x ^{3}-5x ^{2}+19)/\ln (x-2)=3\]\[\ln (x ^{3}-5x ^{2}+19)=3\ln (x-2)=\ln (x-2) ^{3}\]both sides now have a log which can be removed:\[x ^{3}-5x ^{2}+19=(x-2) ^{3}=x ^{3}-6x ^{2}+12x-8\]\[x ^{2}-12x+27=0\]\[(x-3)(x-9)=0\]so x=3 or x=9

Answer 2

Thank you so much!