Condense the logarithm k log a+3log c Answer: log(◻)

Identify Properties: Identify the properties used to condense the logarithm. The properties used to condense the logarithm are the power rule and the product rule for logarithms. The power rule states that n * log_b(x) = log_b(x^n), and the product rule states that log_b(x) + log_b(y) = log_b(xy).Apply Power Rule: Apply the power rule to each term. Using the power rule, we can rewrite k log a as log(a^k) and 3 log c as log(c^3).Apply Product Rule: Apply the product rule to combine the logarithms. Using the product rule, we can combine log(a^k) and log(c^3) into a single logarithm: log(a^k * c^3).Write Final Expression: Write the final condensed logarithmic expression. The final condensed logarithmic expression is log(a^k * c^3).

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Condense the logarithm

k log a+3log c
Answer:
log(◻)

Condense the logarithm $\newline$ $k \log a+3 \log c$ $\newline$ Answer: $\log (\square)$

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Algebra 2

Quotient property of logarithms

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Q. Condense the logarithm

\newline

k \log a+3 \log c

\newline

Answer:

\log (\square)

Identify Properties: Identify the properties used to condense the logarithm. The properties used to condense the logarithm are the power rule and the product rule for logarithms. The power rule states that $n \cdot \log_b(x) = \log_b(x^n)$ , and the product rule states that $\log_b(x) + \log_b(y) = \log_b(xy)$ .
Apply Power Rule: Apply the power rule to each term. $\newline$ Using the power rule, we can rewrite $k \log a$ as $\log(a^k)$ and $3 \log c$ as $\log(c^3)$ .
Apply Product Rule: Apply the product rule to combine the logarithms. $\newline$ Using the product rule, we can combine $\log(a^k)$ and $\log(c^3)$ into a single logarithm: $\log(a^k \cdot c^3)$ .
Write Final Expression: Write the final condensed logarithmic expression. $\newline$ The final condensed logarithmic expression is $\log(a^{k} \cdot c^{3})$ .