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I need an expression written for the following logs using "sum, difference, or multiple of logarithms."

a) log[base(2)] ((x^2) - 9)/(x^3))^3

b) log[base(a)]5a^4

Hopefully they are clearly written.



  • math -

    the base doesn't really matter. All logs follow the same rules.

    (a) log(x^2-9) - 9log(x)
    but your parentheses are not balanced, so that's a guess. Could also be

    3(log(x^2-9) - 3log(x))

    (b) log(5) + 4log(a)
    Now, it helps to know that we're using logs base a, since then we have
    log_a(5) + 4

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