Express 5 log7 x − 2 log7 y + log7 xy as a single logarithm

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∻Solution by Steps∻ ‖ step 1 ⋮ Use the properties of logarithms to combine terms: $5 \log_7(x) - 2 \log_7(y) + \log_7(xy)$ can be rewritten using the power rule and product rule for logarithms. ‖ ‖ step 2 ⋮ Apply the power rule: $5 \log_7(x)$ becomes $\log_7(x^5)$ and $-2 \log_7(y)$ becomes $-\log_7(y^2)$. ‖ ‖ step 3 ⋮ Apply the product rule: $\log_7(x^5) + \log_7(xy)$ becomes $\log_7(x^5 \cdot xy)$. ‖ ‖ step 4 ⋮ Combine the terms: $\log_7(x^5 \cdot xy) - \log_7(y^2)$ becomes $\log_7\left(\frac{x^5 \cdot xy}{y^2}\right)$. ‖ ‖ step 5 ⋮ Simplify the expression: $\log_7\left(\frac{x^5 \cdot xy}{y^2}\right)$ simplifies to $\log_7\left(\frac{x^6}{y}\right)$. ‖ ∻Answer∻ ⚹ $\log_7\left(\frac{x^6}{y}\right)$ ⚹ ∻Key Concept∻ ⚹Logarithm Properties⚹ ∻Explanation∻ ⚹The power rule for logarithms states that $a \log_b(c) = \log_b(c^a)$, and the product rule states that $\log_b(c) + \log_b(d) = \log_b(cd)$. These properties are used to combine multiple logarithmic terms into a single logarithm.⚹◊What is the property of logarithms that allows us to combine multiple logarithmic terms into a single logarithm?⍭ Generate me a similar question◊

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