Write the expression as a single logarithm.
$7 \log_{3} (2 y + 1) + \frac{1}{2} \log_{3} (y + 6)$
$\log_{i]} (◻)$

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So, the expression $7 \log_{3} (2 y + 1) + \frac{1}{2} \log_{3} (y + 6)$ simplifies to $\log_{3} ((2 y + 1)^{7} (y + 6)^{\frac{1}{2}})$ .

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Step 1 ：We are given the expression $7 \log_{3} (2 y + 1) + \frac{1}{2} \log_{3} (y + 6)$ .

Step 2 ：We can use the properties of logarithms to simplify this expression. The property $k \log_{b} (m) = \log_{b} (m^{k})$ allows us to move a coefficient into the argument as an exponent.

Step 3 ：Applying this property to each term, we get $\log_{3} (2 y + 1)^{7} + \log_{3} (y + 6)^{\frac{1}{2}}$ .

Step 4 ：We can then use the property $\log_{b} (m n) = \log_{b} (m) + \log_{b} (n)$ to combine the two logarithms into a single logarithm of the product of the arguments.

Step 5 ：Doing so, we get $\log_{3} ((2 y + 1)^{7} (y + 6)^{\frac{1}{2}})$ .

Step 6 ：So, the expression $7 \log_{3} (2 y + 1) + \frac{1}{2} \log_{3} (y + 6)$ simplifies to $\log_{3} ((2 y + 1)^{7} (y + 6)^{\frac{1}{2}})$ .

Write the expression as a single logarithm.7log3⁡(2y+1)+12log3⁡(y+6)logi]⁡(◻)

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Write the expression as a single logarithm.
$7 \log_{3} (2 y + 1) + \frac{1}{2} \log_{3} (y + 6)$
$\log_{i]} (◻)$