Question

Let f be the function defined by f(x)=ln(3x=2)^k for some positive constant k. If f'(2)=3, what is the value of k?

Answer 1

Use chain rule a couple of times to solve for the derivative, then see what value of k will give you f'(2)=3. What do you have so far in terms of your derivative?

Answer 2

Also, is it supposed to be \[f(x)=\ln((3x+2)^k)\] or \[f(x)=(\ln(3x+2))^k\] Because those are two very different functions and it isn't fully clear from your notation which function you are using.

Answer 3

\[(\ln3)/\ln8\]

Answer 4

The first eqaution

Answer 5

That was my possible answer

Answer 6

Hmm, not quite right. What did you get as a derivative? Note that this problem will be much simpler if you initially use the identity \[f(x)=\ln(3x+2)^k=k\ln(3x+2)\]

Answer 7

so could it possibly be 8

Answer 8

That it is! Good job!