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Apply the logarithm product rule, b M + b N = _b (MN), to the first two terms.

Mathematics

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Answer

log⁡a(xyz)\log_a \left(\frac{xy}{z}\right)

Step-by-step solution

2 steps

  1. Apply the logarithm product rule, log⁡bM+log⁡bN=log⁡b(MN)\log_b M + \log_b N = \log_b (MN), to the first two terms.

    log⁡ax+log⁡ay=log⁡a(xy)\log_a x + \log_a y = \log_a (xy)

  2. Apply the logarithm quotient rule, log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right), to the result from Step 1 and the third term.

    log⁡a(xy)−log⁡az=log⁡a(xyz)\log_a (xy) - \log_a z = \log_a \left(\frac{xy}{z}\right)

    The expression as a single logarithmic term is:

    log⁡a(xyz)\log_a \left(\frac{xy}{z}\right)
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