# Homework Help: CALC AB problems

1. Apr 14, 2009

### coookiemonste

1. The problem statement, all variables and given/known data
Let f be the functions f(x)=ln(3x+2)^k for some positibe constant k.
If f'(2)=3, what is the value of k?
the answer is 8,but i dont think i am taking the derivative right.

2. Relevant equations
?

3. The attempt at a solution
f'(x)=3k*ln(3x+2)^(k-1)/(3x+2)
then i plugged in (2,3) into the derivative above.
and i got k=8/(ln8)(8^(k-1))

2. Apr 14, 2009

### Pengwuino

The derivative is correct, but the answer is not 8. If you plug in (2,3) into your derivative with k=8, you will get a contradiction.

3. Apr 15, 2009

### coookiemonste

my ap book says the answer is 8, however it may be wrong.
but how would you find the value of k?
i am not allowed to use a calculator with this problem.

4. Apr 15, 2009

### rock.freak667

try using the fact that

$$log_a b^r=rlog_a b$$

5. Apr 15, 2009

AH!
thank you!