Question

WILL BECOME A FAN AND A GIVEL A MEDAL
Let f(x)= ln(3x+2)^k for some positive constant k. If f'(2)=3, what is the value of k?
(A) ln3/ln8
(B) ln8
(C) 4
(D) 8
(E) 16

Answer 1

first you know that
\[\ln(3x+2)^k=k\ln(3x+2)\]

Answer 2

the derivative is therefore
\[\frac{3k}{3x+2}\]
replace \(x\) by \(2\), set the result equal to \(3\) and solve for \(k\)

Answer 3

I did that \[3=\frac{ 3k }{ 3(2)+2 } =\frac{ 3k }{ 8 }\]
then I multiplied the 8 to the other side
\[18 \times 3= 3k\]
then I divided the 3
\[18=k\]
and that is not any of the choices. Can anyone see my mistake?