Condense the logarithm y log c+z log q Answer: log(◻)

Identify Properties: Identify the properties of logarithms that can be used to condense the expression y log c + z log q. The power property of logarithms states that n * log_b(x) = log_b(x^n). We can use this property to rewrite the given expression.Apply Power Property: Apply the power property to each term of the expression. y log c can be rewritten as log c^y and z log q can be rewritten as log q^z. So, y log c + z log q becomes log c^y + log q^z.Combine Terms: Use the product property of logarithms to combine the two logarithms into one. The product property states that log_b(x) + log_b(y) = log_b(xy). We can apply this property to the expression log c^y + log q^z. So, log c^y + log q^z becomes log (c^y * q^z).Write Final Expression: Write the final condensed logarithm expression. The final expression is log (c^y * q^z).

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Condense the logarithm

y log c+z log q
Answer:
log(◻)

Condense the logarithm $\newline$ $y \log c+z \log q$ $\newline$ Answer: $\log (\square)$

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Algebra 2

Evaluate logarithms using properties

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Q. Condense the logarithm

\newline

y \log c+z \log q

\newline

Answer:

\log (\square)

Identify Properties: Identify the properties of logarithms that can be used to condense the expression $y \log c + z \log q$ . The power property of logarithms states that $n \cdot \log_b(x) = \log_b(x^n)$ . We can use this property to rewrite the given expression.
Apply Power Property: Apply the power property to each term of the expression. $\newline$ $y \log c$ can be rewritten as $\log c^y$ and $z \log q$ can be rewritten as $\log q^z$ . $\newline$ So, $y \log c + z \log q$ becomes $\log c^y + \log q^z$ .
Combine Terms: Use the product property of logarithms to combine the two logarithms into one. $\newline$ The product property states that $\log_b(x) + \log_b(y) = \log_b(xy)$ . We can apply this property to the expression $\log c^y + \log q^z$ . $\newline$ So, $\log c^y + \log q^z$ becomes $\log (c^y \cdot q^z)$ .
Write Final Expression: Write the final condensed logarithm expression. $\newline$ The final expression is $\log (c^y \cdot q^z)$ .