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Math Help - Solve Power Equation

  1. #1
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    Solve Power Equation

    I am so lost.. Can somebody help me how to solve this:

    Determine X when:


    2X^4,6 = 512x^0,6
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  2. #2
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    re: Solve Power Equation

    First thing I would do is divide both sides by 2. What do you get?
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  3. #3
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    re: Solve Power Equation

    Quote Originally Posted by Ackbeet View Post
    First thing I would do is divide both sides by 2. What do you get?

    2X^4,6 = 512x^0,6

    I will now divide by 2 on both sides:

    X^2,3 = 256x^0,3

    - Correct?
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  4. #4
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    re: Solve Power Equation

    Correct. Now what do you suppose you could do next? You have x raised to a power on both sides of the equation. You'd like to isolate x on one side of the equation. Is there an operation you could do to both sides of the equation that will move you in that direction?

    [EDIT]: You should only have divided the coefficients by two, not the exponents.
    Last edited by Ackbeet; June 15th 2011 at 10:38 AM.
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  5. #5
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    re: Solve Power Equation

    Quote Originally Posted by Ackbeet View Post
    Correct. Now what do you suppose you could do next? You have x raised to a power on both sides of the equation. You'd like to isolate x on one side of the equation. Is there an operation you could do to both sides of the equation that will move you in that direction?
    I am not quite sure. We just divided on both sides.

    But a little question to the title; you've named it "Exponential Equation" - the subject is a "Power equation"?
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  6. #6
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    re: Solve Power Equation

    Quote Originally Posted by oliverbj View Post
    I am not quite sure. We just divided on both sides.
    You'd like to get rid of the exponents somehow. Do you know a function that converts exponents to something else?

    But a little question to the title; you've named it "Exponential Equation" - the subject is a "Power equation"?
    Perhaps you're right. I'll rename again.
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  7. #7
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    Re: Solve Power Equation

    Quote Originally Posted by oliverbj View Post
    I am so lost.. Can somebody help me how to solve this:

    Determine X when:


    2X^4,6 = 512x^0,6
    \displaystyle \begin{align*}2x^{4.6} &= 512x^{0.6} \\ x^{4.6} &= 256x^{0.6} \\ \frac{x^{4.6}}{x^{0.6}} &= 256 \\ x^{4.6 - 0.6} &= 256 \\ x^4 &= 256 \\ x &= 4 \end{align*}
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  8. #8
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    Re: Solve Power Equation

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*}2x^{4.6} &= 512x^{0.6} \\ x^{4.6} &= 256x^{0.6} \\ \frac{x^{4.6}}{x^{0.6}} &= 256 \\ x^{4.6 - 0.6} &= 256 \\ x^4 &= 256 \\ x &= 4 \end{align*}
    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*}2x^{4.6} &= 512x^{0.6} \\ x^{4.6} &= 256x^{0.6} \\ \frac{x^{4.6}}{x^{0.6}} &= 256 \\ x^{4.6 - 0.6} &= 256 \\ x^4 &= 256 \\ x &= 4 \end{align*}
    Wow, thanks a lot! When it is displayed like that, it seems very simple! I get it now. Thanks again.

    But another question, I have to determine the regulation of the Power Equation, when the following two points, is on the power equations graph:
    (2,4) and (4,32)

    How in earth is that done? Or how do I just get started with it?

    Thanks a lot in advance, what a great forum!
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  9. #9
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    Re: Solve Power Equation

    A "power equation" is of the form y= Ax^k. If y= 4 when x= 2, then 4= A(2^k). If y= 32 when x= 4, 32= A(4^k).

    Solve those two equations for A and k. (Trying eliminating A first by dividing one equation by the other.)
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  10. #10
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    Re: Solve Power Equation

    Quote Originally Posted by oliverbj View Post
    I am so lost.. Can somebody help me how to solve this:

    Determine X when:


    2X^4,6 = 512x^0,6
    2x^{4.6} - 512x^{0.6} = 0

    2x^{0.6}(x^4 - 256) = 0

    2x^{0.6}(x^2+16)(x^2-16) = 0

    2x^{0.6}(x^2+16)(x+4)(x-4) = 0

    three real solutions ...
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  11. #11
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    Re: Solve Power Equation

    Right. What Prove It should have said was

    x^{4.6}= 256x^{0.6}
    If x is not 0
    then \frac{x^{4.6}}{x^{0.6}}= x^4= 256
    x= \pm 4

    so the three real roots are 0, 4 and -4.

    We could also note that x^2= \pm 16 so taking the negative root, x^2= -16 gives the two imaginary roots x= \pm 4i.
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