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Posted by on Wednesday, April 17, 2013 at 8:57am.

Write expression as one logarithm and simplify if appropriate.

log 3√x + log x^4 - log x^3

4 log (x+3) - 5 log (x^2+4) + 1/3 log y

I have these who problems but I don't know where to start. HELP Please.

  • college algebra - , Wednesday, April 17, 2013 at 9:12am

    You are going to use 3 man rules of logs

    1. log(A/B) = logA - logB
    2. Log(AB) = logA + logB
    3. log A^n = nlogA

    log 3√x + log x^4 - log x^3
    = log 3 + log x^(1/2) + 4logx - 3logx
    = log3 + (1/2)logs + logx
    = log3 + (3/2)logx

    2.

    4 log (x+3) - 5 log (x^2+4) + 1/3 log y
    = log (x+3)^4 - log (x^2+4)^5 + log y^(1/3)

    = log [ y^(1/3) (x+3)^4 /(x^2+4)^5 ]

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