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How do ratios of logs in different bases compare?

  1. What is ?

    Use your calculator to evaluate this expression.

  2. What is ?

  3. What do you notice about your answers for parts (a) and (b)? Use the change of base formula to explain your results.

  4. Change into a logarithmic expression using a base of .

    Start with the definition of the logarithm.

    Take the log base of both sides.

    Use the Power Property of Logarithms.

    Notice that this answer shows a very quick way to change bases.