Condense the logarithm log c+x log d Answer: log(◻)

Identify Property: Identify the property used to condense the logarithmic expression. The property used to condense the sum of logarithms is the product property of logarithms. Product property: log_b(m) + log_b(n) = log_b(m * n)Apply Product Property: Apply the product property to the term x log(d). Since x is a coefficient of log(d), we can use the power property of logarithms in reverse to rewrite x log(d) as log(d^x). Power property: n * log_b(m) = log_b(m^n)Combine Terms: Combine log(c) and log(d^x) using the product property. Using the product property from Step 1, we combine log(c) and log(d^x) into a single logarithm. log(c) + log(d^x) = log(c * d^x)Write Final Answer: Write the final answer. The expression log(c) + x log(d) has been condensed into log(c * d^x).

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Condense the logarithm

log c+x log d
Answer:
log(◻)

Condense the logarithm $\newline$ $\log c+x \log d$ $\newline$ Answer: $\log (\square)$

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Precalculus

Power property of logarithms

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Q. Condense the logarithm

\newline

\log c+x \log d

\newline

Answer:

\log (\square)

Identify Property: Identify the property used to condense the logarithmic expression. $\newline$ The property used to condense the sum of logarithms is the product property of logarithms. $\newline$ Product property: $\log_b(m) + \log_b(n) = \log_b(m \cdot n)$
Apply Product Property: Apply the product property to the term $x \log(d)$ . Since $x$ is a coefficient of $\log(d)$ , we can use the power property of logarithms in reverse to rewrite $x \log(d)$ as $\log(d^x)$ . Power property: $n \cdot \log_b(m) = \log_b(m^n)$
Combine Terms: Combine $\log(c)$ and $\log(d^x)$ using the product property. $\newline$ Using the product property from Step $1$ , we combine $\log(c)$ and $\log(d^x)$ into a single logarithm. $\newline$ $\log(c) + \log(d^x) = \log(c \cdot d^x)$
Write Final Answer: Write the final answer. $\newline$ The expression $\log(c) + x \log(d)$ has been condensed into $\log(c \cdot d^x)$ .