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Simplify the logarithmic expression: 3 60

Mathematics

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Answer

log⁡216000\log 216000

Step-by-step solution

3 steps

  1. Apply the power rule of logarithms.

    The power rule states that nlog⁡x=log⁡xnn \log x = \log x^n.
    Applying this rule to the given expression:

    3log⁡60=log⁡6033 \log 60 = \log 60^3

  2. Calculate the value of 60360^3.

    603=60×60×60=3600×60=21600060^3 = 60 \times 60 \times 60 = 3600 \times 60 = 216000

  3. Substitute the calculated value back into the logarithmic expression.

    log⁡603=log⁡216000\log 60^3 = \log 216000

    The simplified expression is:

    log⁡216000\log 216000
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