Condense the logarithm g log c+5log q Answer: log(◻)

Identify Properties: Identify the properties used to condense the logarithmic expression. The expression g log c + 5 log q can be condensed using the power property of logarithms, which states that n * log_b(x) = log_b(x^n).Apply Power Property: Apply the power property to each term. For the first term, g log c, we can write it as log(c^g). For the second term, 5 log q, we can write it as log(q^5).Combine Using Product Property: Combine the two logarithms into a single logarithm using the product property. The product property of logarithms states that log_b(x) + log_b(y) = log_b(xy). Therefore, log(c^g) + log(q^5) can be combined into log(c^g * q^5).Write Final Expression: Write the final condensed logarithmic expression. The final expression is log(c^g * q^5).

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Condense the logarithm

g log c+5log q
Answer:
log(◻)

Condense the logarithm $\newline$ $g \log c+5 \log q$ $\newline$ Answer: $\log (\square)$

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Algebra 2

Quotient property of logarithms

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Q. Condense the logarithm

\newline

g \log c+5 \log q

\newline

Answer:

\log (\square)

Identify Properties: Identify the properties used to condense the logarithmic expression. $\newline$ The expression $g \log c + 5 \log q$ can be condensed using 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 each term. $\newline$ For the first term, $g \log c$ , we can write it as $\log(c^g)$ . $\newline$ For the second term, $5 \log q$ , we can write it as $\log(q^5)$ .
Combine Using Product Property: Combine the two logarithms into a single logarithm using the product property. $\newline$ The product property of logarithms states that $\log_b(x) + \log_b(y) = \log_b(xy)$ . $\newline$ Therefore, $\log(c^g) + \log(q^5)$ can be combined into $\log(c^g \cdot q^5)$ .
Write Final Expression: Write the final condensed logarithmic expression. $\newline$ The final expression is $\log(c^g \cdot q^5)$ .