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Condense the logarithm

k log c-log d
Answer:
log(◻)

Condense the logarithm $\newline$ $k \log c-\log d$ $\newline$ Answer: $\log (\square)$

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Convert between exponential and logarithmic form

Full solution

Q. Condense the logarithm

\newline

k \log c-\log d

\newline

Answer:

\log (\square)

Apply Power Rule: We are given the expression $k \log c - \log d$ and we need to condense it into a single logarithm. $\newline$ According to the properties of logarithms, we can use the power rule which states that $a \log (b^c) = c \log b$ . We can apply this rule in reverse to the term $k \log c$ to rewrite it as $\log(c^k)$ .
Combine Terms: Now we have $\log(c^k) - \log d$ . To combine these two logarithms into one, we use the quotient rule of logarithms, which states that $\log b - \log a = \log(\frac{b}{a})$ . We apply this rule to combine $\log(c^k)$ and $\log d$ .
Apply Quotient Rule: Applying the quotient rule gives us $\log\left(\frac{c^k}{d}\right)$ . This is the condensed form of the given logarithmic expression.

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