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Condense the logarithm

log a+z log g
Answer: 
log(◻)

Condense the logarithm\newlineloga+zlogg \log a+z \log g \newlineAnswer: log() \log (\square)

Full solution

Q. Condense the logarithm\newlineloga+zlogg \log a+z \log g \newlineAnswer: log() \log (\square)
  1. Question Prompt: Question prompt: What is the condensed form of the logarithm expression given by "loga+zlogg\log a + z \log g"?
  2. Recognize Properties: Recognize the properties of logarithms that can be used to condense the expression. The property that allows us to combine two logarithms with the same base and a multiplication between their arguments when they are being added is the product property of logarithms: logb(m)+logb(n)=logb(mn)\log_b(m) + \log_b(n) = \log_b(m*n).
  3. Apply Product Property: Apply the product property to the given logarithmic expression.\newlineWe have loga+zlogg\log a + z \log g, which can be rewritten using the product property as log(agz)\log(a * g^z).
  4. Check for Simplifications: Check for any possible simplifications. In this case, there are no further simplifications that can be made to the expression log(agz)\log(a \cdot g^z).

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