Math

Solve: 19^(x-5)=3^(x+2)
i know you then go: (x-5) log19= (x+2) log3
i just don't know what goes after?

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asked by Maxx
  1. those logs are just numbers, so

    x log19 - 5log19 = x log3 + 2log3
    x(log19-log3) = 2log3 + 5log19

    x =
    2log3 + 5log19
    --------------------
    log19 - log3

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    posted by Steve
  2. expand:
    (x-5) log19= (x+2) log3
    xlog19 - 5log19 = xlog3 + 2log3
    xlog19 - xlog3 = 2log3 + 5log19
    x(log19 - log3) = 2log3 + 5log10
    x = (2log3 + 5log19)/(log19 - log3)
    = appr 9.1663

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    posted by Reiny

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