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Please help, ADVANCED FUNCTIONS

  • Thread starter Acnhduy
  • Start date
  • #1
31
1

Homework Statement


4^x + 6(4^-x) = 5


Homework Equations


log??? since this is the unit we are doing, but i'm not sure if it applies.


The Attempt at a Solution



I was thinking of changing 4^x to a variable like 'a', but 4^-x is not the same so I can't replace that with 'a' as well.
Then I though 4^-x = 1/4 ^x
So
4^x + 6[(1/4)^x] = 5

and I'm lost.
thanks :)
 

Answers and Replies

  • #2
Simon Bridge
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Homework Helper
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You have:

$$4^{x}+6(4^{-x})=5$$ ... is that right?

... and you want to put it into some form that you can integrate or differentiate or something?
You suspect it has something to do with taking a logarithm - so do I :), since ##\log_4(4^x)=x## hugely simplifies the problem.

Your intuition to put ##a=4^x## is a good one - with that substitution you get:
$$a+\frac{6}{a}=5$$ ... which is hard to think about, so put it in standard form.
Hint: multiply both sides by ##a##.
What sort of equation is that?
 
Last edited:
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  • #3
31
1
it is actually,

4^x + 6(1/4)^x = 5
 
  • #4
31
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Quadratic :) thankyou
 
  • #5
Simon Bridge
Science Advisor
Homework Helper
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Well done :)
 

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