# How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log (1/5)^3#?

You can start by rewriting.

Then put the exponent in front:

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To evaluate the logarithm (\log \left(\frac{1}{5}\right)^3) using the Change of Base Formula and a calculator, you can follow these steps:

- Apply the exponent rule for logarithms: (\log_b(a^c) = c \cdot \log_b(a)).
- Rewrite the logarithm using the exponent rule: (\log \left(\frac{1}{5}\right)^3 = 3 \cdot \log \left(\frac{1}{5}\right)).
- Use the Change of Base Formula, which states that (\log_b(a) = \frac{\log_c(a)}{\log_c(b)}), where (c) is any positive number different from 1.
- Choose a convenient base for the logarithm. Typically, calculators use base 10 (denoted as (\log_{10})) or base (e) (natural logarithm, denoted as (\ln)).
- Apply the Change of Base Formula: (\log \left(\frac{1}{5}\right) = \frac{\log\left(\frac{1}{5}\right)}{\log(10)}) or (\log \left(\frac{1}{5}\right) = \frac{\ln\left(\frac{1}{5}\right)}{\ln(10)}).
- Use a calculator to evaluate the logarithm using the chosen base.
- Finally, multiply the result by 3 since we applied an exponent of 3 earlier.

By following these steps, you can accurately evaluate the logarithm (\log \left(\frac{1}{5}\right)^3) using the Change of Base Formula and a calculator.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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