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Math Help - Solution to Exponential equation

  1. #1
    Member Goku's Avatar
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    Solution to Exponential equation

    Can this equation be solved explicitly for x
    y=2.3^x + 7^x
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Solution to Exponential equation

    I think there're no real solutions if you want to solve y=0.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: Solution to Exponential equation

    Quote Originally Posted by Siron View Post
    I think there're no real solutions if you want to solve y=0.
    That is not the question (but you can see that y cannot be zero or negative starting in two lines...)

     y = a^x + b^x

     \ln y = x \ln a + x \ln b

     \ln y = x (\ln a + \ln b)

     \ln y = x (\ln ab)

    Can you take it from here?
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  4. #4
    Member Goku's Avatar
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    Re: Solution to Exponential equation

    If you are given a y solve for x, I am looking for an algorithm
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  5. #5
    Super Member Quacky's Avatar
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    Re: Solution to Exponential equation

    Quote Originally Posted by TheChaz View Post
    That is not the question.

     y = a^x + b^x

     \ln y = x \ln a + x \ln b

     \ln y = x (\ln a + \ln b)

     \ln y = x (\ln ab)

    Can you take it from here?
    Someone needs their morning coffee.

    Let x=2, a=3, b=4
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  6. #6
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    e^(i*pi)'s Avatar
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    Re: Solution to Exponential equation

    Quote Originally Posted by TheChaz View Post
    That is not the question (but you can see that y cannot be zero or negative starting in two lines...)

     y = a^x + b^x

     \ln y = x \ln a + x \ln b

     \ln y = x (\ln a + \ln b)

     \ln y = x (\ln ab)

    Can you take it from here?
    Except \ln(a^x+b^x) \neq x\ln(a) + x\ln(b)
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  7. #7
    Super Member TheChaz's Avatar
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    Re: Solution to Exponential equation

    Quote Originally Posted by Quacky View Post
    Someone needs their morning coffee.

    Let x=2, a=3, b=4
    I must need some coffee... Then y = 25 ??
    Can you come to the punchline - I'm a little tired apparently!
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  8. #8
    Super Member TheChaz's Avatar
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    Re: Solution to Exponential equation

    Quote Originally Posted by e^(i*pi) View Post
    Except \ln(a^x+b^x) \neq x\ln(a) + x\ln(b)
    Oh *^&%& ! Hah... I knew it seemed too easy!

    (edit... I did have a pretty good night last night )
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