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Simplify the numerator using the logarithm property aⁿ = n a.

Mathematics

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3

Step-by-step solution

4 steps

To simplify the expression log⁡27log⁡6−log⁡2\frac{\log 27}{\log 6 - \log 2}:

  1. Simplify the numerator using the logarithm property log⁡an=nlog⁡a\log a^n = n \log a.

    log⁡27=log⁡(33)=3log⁡3\log 27 = \log (3^3) = 3 \log 3

  2. Simplify the denominator using the logarithm property log⁡a−log⁡b=log⁡(ab)\log a - \log b = \log \left(\frac{a}{b}\right).

    log⁡6−log⁡2=log⁡(62)=log⁡3\log 6 - \log 2 = \log \left(\frac{6}{2}\right) = \log 3

  3. Substitute the simplified numerator and denominator back into the original expression.

    3log⁡3log⁡3\frac{3 \log 3}{\log 3}

  4. Cancel out the common term log⁡3\log 3.

    33
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