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Log help

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If a^3 + 3ab(a+b+3)+b^3 = 10ab, show that log (a+b)=1/3(log a + log b). Please show step by step. Thank you!

  • Log help -

    a^3 + 3ab(a+b+3) + b^3 = 10ab

    a^3 + 3a^2b + 3ab^2 + 9ab + b^3 = 10ab
    a^3 + 3a^2b + 3ab^2 + b^3 = ab
    (a+b)^3 = ab
    take log of both sides

    log (a+b)^3= log ab
    3 log(a+b) = log a + log b
    log (a+b) = (1/3)(log a + log b)

    Q.E.D.

  • Log help -

    Thank you!

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