Algebra

Please express in terms of sums and differences in logarithms.

log a x^3 y^2 z

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  1. Add the logs of every term in the product. For the x^3 term, you get 3logx. You do the rest. Let us know if you want your answer checked

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  2. 1 log a 3log x 2log y 1 logz Is this correct?

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  3. No. You have to add the logs of each term. Remember that
    log (abc) = log a + log b + log c etc.

    Your answer should be
    log (a x^3 y^2 z) = log a + 3 log x + 2 log y + log z

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  4. Please express in terms of sums and differences in logarithms.

    log a x^3 y^2 z

    For log_a (x^3) we can use the rule

    log_b (m^n) = nlog_b (x).

    The log_a (x^3) becomes 3xlog_a (x).

    ===================================

    We usethe same rule for y^2.

    y^2 becomes 2log_y.

    And finally, z becomes log_z.

    We now use the sum rule:

    log_b(mn) = log_b(m) + log_b(n).

    3log_a(x) + 2log_y + log_z

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