Question
\( \log 40+\log 25=\square \) (Simplify your answer.)
Ask by Carrillo Stanley. in Saudi Arabia
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\log 40 + \log 25 = 3
\]
Solution
We start by using the logarithm property:
\[
\log a + \log b = \log (ab)
\]
So,
\[
\log 40 + \log 25 = \log (40 \times 25)
\]
Next, we calculate the product:
\[
40 \times 25 = 1000
\]
Thus,
\[
\log (40 \times 25) = \log 1000
\]
Since \(1000 = 10^3\), we have:
\[
\log 1000 = \log (10^3)
\]
And by the logarithmic identity \(\log (10^3) = 3\), the final answer is:
\[
\log 40 + \log 25 = 3
\]
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Simplify this solution Mind Expander
To simplify \( \log 40 + \log 25 \), we can use the property of logarithms that states \( \log a + \log b = \log(ab) \). Thus, we have: \[ \log 40 + \log 25 = \log(40 \times 25) = \log(1000). \] Since \( 1000 = 10^3 \), we can further simplify this to: \[ \log(1000) = \log(10^3) = 3. \] So, \( \log 40 + \log 25 = 3 \).
