Question
Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. \( \log \left(\mathrm{A}^{-3}\right) \) \( \log \left(\mathrm{A}^{-3}\right)=\square \)
Ask by Moreno Long. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\log \left(\mathrm{A}^{-3}\right) = -3 \log \mathrm{A}
\]
Solution
1. Use the power rule for logarithms:
\[
\log \left(\mathrm{A}^{-3}\right) = -3 \log \mathrm{A}
\]
2. Thus, the expanded form is:
\[
\log \left(\mathrm{A}^{-3}\right) = -3 \log \mathrm{A}
\]
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Simplify this solution Bonus Knowledge
The expression can be expanded using the power rule of logarithms, which states that \( \log(a^b) = b \cdot \log(a) \). Applying this rule, we get: \(\log \left(\mathrm{A}^{-3}\right) = -3 \cdot \log(A)\). Now let's evaluate the logarithmic expression. If we assume \( \log(A) = x \) (where \( A \) is a positive number), then we have: \(\log \left(\mathrm{A}^{-3}\right) = -3x\). So, the expanded expression is \(-3 \cdot \log(A)\).
