Write the expression as a single logarithm.
$7 \log_{c} (7 x + 1) + \frac{1}{2} \log_{c} (x + 8)$

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The simplified expression is $\log_{c} ((7 x + 1)^{7} (x + 8)^{\frac{1}{2}})$

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Step 1 ：Given the expression $7 \log_{c} (7 x + 1) + \frac{1}{2} \log_{c} (x + 8)$

Step 2 ：We can use the properties of logarithms to simplify this expression. The properties are as follows: $a \log_{b} (c) = \log_{b} (c^{a})$ and $\log_{b} (c) + \log_{b} (d) = \log_{b} (c d)$

Step 3 ：Applying the first property to both terms, we get $\log_{c} ((7 x + 1)^{7}) + \log_{c} ((x + 8)^{1 / 2})$

Step 4 ：Then, applying the second property to combine the two terms into a single logarithm, we get $\log_{c} ((7 x + 1)^{7} * (x + 8)^{1 / 2})$

Step 5 ：The simplified expression is $\log_{c} ((7 x + 1)^{7} (x + 8)^{\frac{1}{2}})$

Write the expression as a single logarithm.7logc⁡(7x+1)+12logc⁡(x+8)

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Write the expression as a single logarithm.
$7 \log_{c} (7 x + 1) + \frac{1}{2} \log_{c} (x + 8)$