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Condense the logarithm

g log a+log d
Answer:
log(◻)

Condense the logarithm $\newline$ $g \log a+\log d$ $\newline$ Answer: $\log (\square)$

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Convert between exponential and logarithmic form

Full solution

Q. Condense the logarithm

\newline

g \log a+\log d

\newline

Answer:

\log (\square)

Question Prompt: Question prompt: Condense the expression $g \log a + \log d$ into a single logarithm.
Combine Logarithms: Apply the logarithm property that allows us to combine two logarithms with the same base that are being added into a single logarithm by multiplying their arguments. $\newline$ The property is $\log_b(m) + \log_b(n) = \log_b(m*n)$ , where $b$ is the base of the logarithms.
Rewrite Coefficient: Use the property from Step $1$ to combine $g \log a + \log d$ . Since $g$ is a coefficient of $\log a$ , we can rewrite it as $\log a^g$ using the property that $g\log_b(m) = \log_b(m^g)$ . So, $g \log a + \log d = \log a^g + \log d$ .
Final Simplification: Now apply the property from Step $1$ to the expression $\log a^g + \log d$ . This gives us $\log(a^g \cdot d)$ .

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