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  1. How do ratios of logs in different bases compare? Homework Help ✎

    1. What is ?

    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 log2(7) into a logarithmic expression using a base of 5.

Use your calculator to evaluate this expression.

Start with the definition of the logarithm.
log27 = x
2x = 7

Take the log base 5 of both sides.
log5(2x) = log57

Use the Power Property of Logarithms.
x(log52) = log57

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