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Condense the logarithm

8log c-4log d
Answer:
log(◻)

Condense the logarithm $\newline$ $8 \log c-4 \log d$ $\newline$ Answer: $\log (\square)$

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Convert between exponential and logarithmic form

Full solution

Q. Condense the logarithm

\newline

8 \log c-4 \log d

\newline

Answer:

\log (\square)

Apply Power Rule: We are given the expression $8\log c - 4\log d$ and we need to condense it into a single logarithm. $\newline$ According to the power rule of logarithms, $a\log_b(x) = \log_b(x^a)$ , we can apply this rule to both terms.
Combine Terms: Apply the power rule to the first term: $8\log c$ becomes $\log(c^8)$ . Apply the power rule to the second term: $4\log d$ becomes $\log(d^4)$ .
Apply Quotient Rule: Now we have $\log(c^8) - \log(d^4)$ . According to the quotient rule of logarithms, $\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)$ , we can combine these two logarithms into one.
Final Condensed Form: Combine the two logarithms using the quotient rule: $\log(c^8) - \log(d^4)$ becomes $\log\left(\frac{c^8}{d^4}\right)$ .
Final Condensed Form: Combine the two logarithms using the quotient rule: $\log(c^8) - \log(d^4)$ becomes $\log\left(\frac{c^8}{d^4}\right)$ .The expression is now fully condensed into a single logarithm.

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