Question
Use properties of logarithms to evaluate the expression. \( \log 50+\log 2 \) \( \square \) \( \square \)
Ask by Bartlett Sandoval. in the United States
Mar 14,2025
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\(\log 100 = 2\)
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When you combine logarithms using the property \( \log a + \log b = \log(ab) \), you can simplify \( \log 50 + \log 2 \) to \( \log(50 \times 2) \). This gives you \( \log 100 \). Now, \( \log 100 \) can be evaluated further since 100 is equal to \( 10^2 \). Thus, using another logarithm property \( \log(a^b) = b \log a \), you find \( \log 100 = \log(10^2) = 2 \log 10 \). Since \( \log 10 = 1 \), this simplifies to \( 2 \). So, the expression evaluates to \( 2 \).