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Pre-Cal

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Solve the following logarithmic equation. Exact words only:
log 3(x+4) = 2+log3(x-20)
the 3 in the part of log (3)should be lower just didn't know how to type it in here

  • Pre-Cal - ,

    log3 (x+4) - log3 (x-20) = 2 , where clearly x > 20
    log3 ( (x+4)/(x-20) ) = 2
    (x+4)/(x-20) = 3^2 = 9
    9x - 180 = x+4
    8x = 184
    x = 23

    check:
    LS = log3 27 = 3
    RS = 2 + log3 3
    = 2 + 1 = 3 = LS

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