Write the expression as a single logarithm.
$5 \log_{c} w - \frac{1}{3} \log_{c} z + 7 \log_{c} x$

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So, the expression $5 \log_{c} w - \frac{1}{3} \log_{c} z + 7 \log_{c} x$ can be written as a single logarithm as $\log_{c} \frac{w^{5} x^{7}}{z^{1 / 3}}$ .

Steps

Step 1 ：First, we apply the power rule of logarithms, which states that $\log_{b} m^{n} = n \log_{b} m$ . This gives us $\log_{c} w^{5} - \log_{c} z^{1 / 3} + \log_{c} x^{7}$ .

Step 2 ：Next, we apply the product rule of logarithms, which states that $\log_{b} m n = \log_{b} m + \log_{b} n$ . This gives us $\log_{c} (w^{5} x^{7}) - \log_{c} z^{1 / 3}$ .

Step 3 ：Finally, we apply the quotient rule of logarithms, which states that $\log_{b} \frac{m}{n} = \log_{b} m - \log_{b} n$ . This gives us $\log_{c} \frac{w^{5} x^{7}}{z^{1 / 3}}$ .

Step 4 ：So, the expression $5 \log_{c} w - \frac{1}{3} \log_{c} z + 7 \log_{c} x$ can be written as a single logarithm as $\log_{c} \frac{w^{5} x^{7}}{z^{1 / 3}}$ .

Write the expression as a single logarithm.5logc⁡w−13logc⁡z+7logc⁡x

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Write the expression as a single logarithm.
$5 \log_{c} w - \frac{1}{3} \log_{c} z + 7 \log_{c} x$