Solving CALC AB Problems for f'(2)=3

[coookiemonste]

Homework Statement

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 don't think i am taking the derivative right.

Homework Equations

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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))

 

[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.

 

[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.

 

[rock.freak667]

try using the fact that

log_a b^r=rlog_a b

 

[coookiemonste]

AH!
thank you!