algebra

Can anyone solve this without expanding:

(2x+9)**(1/5) = (9x-5)**(1/7)

Thanks in advance
Su

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asked by su
  1. Does the ** represent multiplication (x) or raising to an exponent (^) ??

    Your notation needs to be explained.

    If you mean
    (2x+9)/5 = (9x-5)/7, then
    14x +63 = 45x -25
    31x = 88
    x = 88/31

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    posted by drwls
  2. No its an exponent not a fraction.

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    posted by su
  3. In that case
    (2x+9)^(1/5) = (9x-5)^(1/7)
    9x-5 = (2x+9)^(7/5)
    9x = (2x+9)^(7/5) + 5
    x = 0.2605
    (I had to solve that by iteration)

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    posted by drwls
  4. If we put back the value .2605 in the equation and use the calculator we get on LHS (2*.2605 +9)^(1/5) = 1.5694
    but on RHS( 9*.2605 -5)^(1/7) we get = -1.1497
    so by iteration is also not correct ..

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    posted by su
  5. I made up a "primitive" program in Quick-Basic and got a value of x = appr. -35.75

    for that value
    LS = (-62.5)^(1/5) = -2.286525
    RS = ( -326.75)^(1/7) = -2.286513

    not bad, eh?

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    posted by Reiny
  6. I Still should be able to solve algebrically for a solution of -35.75 -This basically is a radical program.

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    posted by su

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