Condense the logarithm log a-6log c Answer: log(◻)

Identify Property: Identify the property used to condense the logarithmic expression. The expression log a - 6 log c involves a difference of logarithms, where one of the terms is a multiple of a logarithm. To condense this expression, we use the power property of logarithms, which states that n * log_b(x) = log_b(x^n).Apply Power Property: Apply the power property to the term with the multiple. The power property allows us to rewrite 6 log c as log(c^6). This is because multiplying a logarithm by a number is equivalent to raising the argument of the logarithm to the power of that number.Combine Using Quotient Property: Combine the two logarithms into a single logarithm using the quotient property. The quotient property of logarithms states that log_b(P) - log_b(Q) = log_b(P/Q). We can apply this property to combine log a and log(c^6) into a single logarithm.Write Final Expression: Write the final condensed logarithmic expression. Using the quotient property, we combine the two logarithms into one: log a - log(c^6) = log(a/c^6).

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Condense the logarithm

log a-6log c
Answer:
log(◻)

Condense the logarithm $\newline$ $\log a-6 \log c$ $\newline$ Answer: $\log (\square)$

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Algebra 2

Quotient property of logarithms

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Q. Condense the logarithm

\newline

\log a-6 \log c

\newline

Answer:

\log (\square)

Identify Property: Identify the property used to condense the logarithmic expression. $\newline$ The expression $\log a - 6 \log c$ involves a difference of logarithms, where one of the terms is a multiple of a logarithm. To condense this expression, we use the power property of logarithms, which states that $n \cdot \log_b(x) = \log_b(x^n)$ .
Apply Power Property: Apply the power property to the term with the multiple. $\newline$ The power property allows us to rewrite $6 \log c$ as $\log(c^6)$ . This is because multiplying a logarithm by a number is equivalent to raising the argument of the logarithm to the power of that number.
Combine Using Quotient Property: Combine the two logarithms into a single logarithm using the quotient property. $\newline$ The quotient property of logarithms states that $\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)$ . We can apply this property to combine $\log a$ and $\log(c^6)$ into a single logarithm.
Write Final Expression: Write the final condensed logarithmic expression. $\newline$ Using the quotient property, we combine the two logarithms into one: $\log a - \log(c^6) = \log\left(\frac{a}{c^6}\right)$ .