To combine the expression \( 2\log(3) + \log(8) \) into a single logarithm, we can use the properties of logarithms.
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The first step involves using the power rule of logarithms, which states that \( a \log(b) = \log(b^a) \). We can rewrite \( 2\log(3) \) as: \[ \log(3^2) = \log(9) \]
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Now we can rewrite the original expression: \[ 2\log(3) + \log(8) = \log(9) + \log(8) \]
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Next, we use the product rule of logarithms, which states that \( \log(a) + \log(b) = \log(ab) \): \[ \log(9) + \log(8) = \log(9 \cdot 8) \]
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Now, calculate \( 9 \cdot 8 \): \[ 9 \cdot 8 = 72 \]
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Thus, we have: \[ \log(9) + \log(8) = \log(72) \]
So, the expression \( 2\log(3) + \log(8) \) as a single logarithm is: \[ \log(72) \]
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