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What is the purpose of the change of base formula? Why is it useful when using a calculator? Choose ALL correct answers. The formula allows us to rewrite a logarithm that is in terms of common or natural logs as a logarithm in other bases so a calculator can be used to evaluate it Most calculators have the capability of evaluating only common and natural logarithms There is no good purpose for this formula The formula allows us to rewrite a logarithm in terms of logs written with another base

Ask by Ward Hodges. in the United States
Feb 25,2025

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The change of base formula allows us to rewrite logarithms in terms of common or natural logs, which most calculators can evaluate. It's useful because it lets us find the value of logarithms in other bases using only common or natural logarithms.

Solución

The correct answers regarding the purpose of the change of base formula and its usefulness when using a calculator are: 1. **The formula allows us to rewrite a logarithm that is in terms of common or natural logs as a logarithm in other bases so a calculator can be used to evaluate it.** 2. **Most calculators have the capability of evaluating only common and natural logarithms.** 3. **The formula allows us to rewrite a logarithm in terms of logs written with another base.** The change of base formula is particularly useful because it enables the evaluation of logarithms in bases that are not directly supported by most calculators, which typically only handle base 10 (common logarithm) and base e (natural logarithm).

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The Deep Dive

The change of base formula is a lifesaver when it comes to using calculators! Most calculators are equipped to handle just common (base 10) and natural (base e) logarithms, so when you're faced with a different base—like log base 2 or any other—it can feel like a hassle. The formula allows you to convert those tricky logarithms into forms that your trusty calculator can handle, giving you accurate results in a flash. Imagine you're trying to solve a complex equation involving logarithms, but your calculator is stubbornly refusing to cooperate with your chosen base. By using the change of base formula, you can transform that pesky log into a form that allows you to easily calculate it using the logarithmic functions available on your device. This makes you feel like a math wizard, turning frustrations into triumphs—all while ensuring your calculations stay accurate and within reach!

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