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Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, \( \log 125+\log 8 \) \( \log 125+\log 8=\square \) (Simplify your answer.)

Ask by Owen Wheeler. in the United States
Mar 21,2025

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\( \log 125 + \log 8 = \log 1000 \)

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To condense the expression, you can use the property of logarithms that states \( \log a + \log b = \log(ab) \). So, you would have: \( \log 125 + \log 8 = \log(125 \cdot 8) \). Now, calculate \( 125 \cdot 8 = 1000 \). Therefore, the expression simplifies to: \( \log 1000 \). Since 1000 is equal to \( 10^3 \), you can further simplify it to: \( \log 1000 = 3 \). So the final condensed expression is: \( \log 125 + \log 8 = \log 1000 = 3 \).

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