Write the expression as a single logarithm. 7log_(c)(w-7)-3log_(c)(w+2)

Apply Power Rule: Apply the power rule of logarithms to both terms. The power rule states that log_b(a^n) = n*log_b(a). We can apply this rule in reverse to move the coefficients of the logarithms up as exponents of their arguments. 7log_c(w-7) becomes log_c((w-7)^7) 3log_c(w+2) becomes log_c((w+2)^3)Apply Quotient Rule: Apply the quotient rule of logarithms to combine the two logarithms into one. The quotient rule states that log_b(a) - log_b(c) = log_b(a/c). We can use this rule to combine our two logarithms into a single logarithm. log_c((w-7)^7) - log_c((w+2)^3) becomes log_c(((w-7)^7)/(w+2)^3)

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Write the expression as a single logarithm.
7log_(c)(w-7)-3log_(c)(w+2)

Write the expression as a single logarithm. $\newline$ $7 \log _{c}(w-7)-3 \log _{c}(w+2)$

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Precalculus

Properties of logarithms: mixed review

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Q. Write the expression as a single logarithm.

\newline

7 \log _{c}(w-7)-3 \log _{c}(w+2)

Apply Power Rule: Apply the power rule of logarithms to both terms. $\newline$ The power rule states that $\log_b(a^n) = n\log_b(a)$ . We can apply this rule in reverse to move the coefficients of the logarithms up as exponents of their arguments. $\newline$ $7\log_c(w-7)$ becomes $\log_c((w-7)^7)$ $\newline$ $3\log_c(w+2)$ becomes $\log_c((w+2)^3)$
Apply Quotient Rule: Apply the quotient rule of logarithms to combine the two logarithms into one. $\newline$ The quotient rule states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ . We can use this rule to combine our two logarithms into a single logarithm. $\newline$ $\log_c\left((w-7)^7\right) - \log_c\left((w+2)^3\right)$ becomes $\log_c\left(\frac{(w-7)^7}{(w+2)^3}\right)$