Question
valuate: \( \log 15+\log 20= \) \[ \begin{array}{llllll}0.904 & \text { b. } 2.477 & \text { c. } 1.544 & \text { d. } & -0.904\end{array} \]
Ask by Chadwick Tran. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The value of \( \log 15 + \log 20 \) is approximately 2.477.
Solution
To evaluate \( \log 15 + \log 20 \), we'll use the logarithmic property that states:
\[
\log a + \log b = \log (a \times b)
\]
Applying this property:
\[
\log 15 + \log 20 = \log (15 \times 20) = \log 300
\]
Now, calculating \( \log 300 \) (assuming base 10):
\[
\log 300 \approx 2.477
\]
**Therefore, the correct answer is:**
**b. 2.477**
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Simplify this solution Mind Expander
To evaluate \( \log 15 + \log 20 \), we can use the property of logarithms that states \( \log a + \log b = \log(ab) \). So, we can rewrite this as: \[ \log(15 \times 20) = \log(300). \] Now, we need to calculate \( \log(300) \). We can break it down as: \[ 300 = 3 \times 100 = 3 \times 10^2, \] so, \[ \log(300) = \log(3 \times 10^2) = \log 3 + \log(10^2) = \log 3 + 2. \] Using the approximate value \( \log 3 \approx 0.477 \) (base 10 logarithm), we find: \[ \log(300) \approx 0.477 + 2 \approx 2.477. \] Thus, the answer is \( \log 15 + \log 20 \approx 2.477 \), which corresponds to answer choice **b**.
