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solve 3^x=4^(x-2)

  • Maths -

    take ln of both sides
    ln (3^x) = ln (4^(x-2))
    x(ln3) = (x-2)(ln4)
    = x(ln4) - 2ln4
    xln3 - xln4 = -2ln4
    x(ln3 - ln4) = -2ln4
    x = -2ln4/(ln3-ln4)
    or
    x = 2ln4/(ln4 - ln3)

    if get appr. 9.638

    check:
    3^9.638 = appr. 39672.63
    4^7.638 = 39676.6
    ----- close enough using only 3 decimals, if I use my calculator's memory and store the full value of x, my error is 5.9x10^-6

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