Question
Question 5 (4 points) 1. Express \( \log 5-\log 12 \) as a single logarithm: 2. Using a calculator to simplify, this would equal Blank 1: Blank 2:
Ask by Rojas Lane. in the United States
Feb 10,2025
Upstudy AI Solution
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Answer
1. \( \log 5 - \log 12 = \log\left(\frac{5}{12}\right) \)
2. Using a calculator, this equals approximately -0.38.
Blank 1: \( \log\left(\frac{5}{12}\right) \)
Blank 2: -0.38
Solution
1. Using the quotient rule for logarithms, we have:
log 5 - log 12 = log(5/12).
2. Using a calculator (assuming base-10 logarithms), log(5/12) ≈ -0.38.
Blank 1: log(5/12)
Blank 2: -0.38
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Simplify this solution Mind Expander
To express \( \log 5 - \log 12 \) as a single logarithm, you can use the property that states \( \log a - \log b = \log \left( \frac{a}{b} \right) \). Applying this property here, we get: \[ \log 5 - \log 12 = \log \left( \frac{5}{12} \right). \] For the second part, using a calculator to simplify \( \log \left( \frac{5}{12} \right) \) gives us approximately -0.07918. Blank 1: \( \log \left( \frac{5}{12} \right) \) Blank 2: -0.07918
