What is the solution for x in 2x^(1/4) = 64/x using indices?

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In summary, the person is struggling to solve the equation 2x^ \frac{1} {4} = \frac{64} {x} and is looking for guidance. They realize they need to multiply both sides by x and use the property of adding exponents when multiplying, but initially make a mistake and then correct it. They eventually solve the equation and thank those who helped them.
  • #1
Mo
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Indices.Again i think I've got close to the answer, it just does not want to show its self! A push in the right direction would be appreciated ... here's the problem:

[tex]2x^ \frac{1} {4} = \frac{64} {x} [/tex]

Regards
Mo
 
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  • #2
Multiply both sides by x. Remember that x = x^1 and x^a * x^b = x^(a + b) for all a, b.
 
  • #3
Hmm i multiplied both sides by x ..i think the answer is:

[tex]2x^ \frac{2} {4} = 64 [/tex] right?? ... carrying on ...

then divide both sides by 2 ..so we are left with ..

[tex]x ^\frac {2} {4} = 32 [/tex]

am i along the right lines here??
 
  • #4
How did you get [itex]x^{2/4}[/itex]?
 
  • #5
hmm, i multiple both sides by x so

[tex]2x^ \frac {1} {4} X x = 2x^ \frac {1} {4} X x^1[/tex]

and since we add the indices when multiplying i get 2 no?
 
  • #6
oh lol i think i just spotted it ..
 
  • #7
edit: should be 1.25 right?

Ack - stupid mistakes , i got it now.Completely overlooked it .. :blushing: .

Thanks both :smile:
 

FAQ: What is the solution for x in 2x^(1/4) = 64/x using indices?

What is the equation?

The equation is 2x^(1/4) = 64/x.

What is x?

x is the unknown variable in the equation that we are trying to solve for.

How do you solve the equation?

To solve the equation, we can first multiply both sides by x to get rid of the fraction. This gives us 2x^(5/4) = 64. Then, we can take the fourth root of both sides to isolate x. This gives us x = (64/2)^(4/5) = 8^4 = 4096.

Are there any other solutions?

Yes, there are two other solutions for x: -4096 and -i*8^(4/5), where i is the imaginary unit.

Why is it important to find x?

Finding x helps us understand the relationship between the two sides of the equation and can be useful in solving other problems. It also allows us to check our work and ensure that the equation is balanced.

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