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Algebra 2

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-Explain the difference between log base b of m plus log base b of n and log base b (m+n). Are they equivalent?

-Explain the difference between log base b (mn) and ( log base b of m)(log base b of n). Are they equivalent?

  • Algebra 2 -

    Is logb m + logb = logb(m+n)

    no they are not, since
    logbm + logbn = logb(mn)

    All we need is ONE counter-example to show that your statement is false.

    Assume that
    logb m + logb = logb(m+n)

    then it should be true for all values of b, m, and n within the domain of log definitions.

    let's take some values for which we know the exact values
    e.g.
    log2 8 + log2 16
    = 3 + 4
    = 7
    and log2 (8+16)
    = log2 24 ≠ 7

    Use a similar argument and example for your second question.

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