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CALC AB problems

  • #1

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 dont think i am taking the derivative right.



Homework Equations


?


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))
 

Answers and Replies

  • #2
Pengwuino
Gold Member
4,989
15
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
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
rock.freak667
Homework Helper
6,230
31
try using the fact that

[tex]log_a b^r=rlog_a b[/tex]
 
  • #5
AH!
thank you!
 

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