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Condense the logarithm

y log d-log x
Answer:
log(◻)

Condense the logarithm $\newline$ $y \log d-\log x$ $\newline$ Answer: $\log (\square)$

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Convert between exponential and logarithmic form

Full solution

Q. Condense the logarithm

\newline

y \log d-\log x

\newline

Answer:

\log (\square)

Identify Logarithmic Expression: Question prompt: What is the condensed form of the logarithmic expression $y \log d - \log x$ ?
Apply Power Rule: Apply the power rule of logarithms to the term $y \log d$ , which states that $\log_b(a^c) = c \log_b(a)$ . Here, we rewrite $y \log d$ as $\log(d^y)$ .
Use Quotient Rule: Use the quotient rule of logarithms, which states that $\log_b(a) - \log_b(c) = \log_b(\frac{a}{c})$ , to combine the two logarithmic terms. $\newline$ We have $\log(d^y) - \log x$ , which can be written as $\log(\frac{d^y}{x})$ .
Check for Simplifications: Check for any possible simplifications of the expression inside the logarithm. In this case, there are no further simplifications, so the expression $\log(\frac{d^y}{x})$ is already in its simplest form.

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