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Condense the logarithm

7log a-x log d
Answer:
log(◻)

Condense the logarithm $\newline$ $7 \log a-x \log d$ $\newline$ Answer: $\log (\square)$

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Convert between exponential and logarithmic form

Full solution

Q. Condense the logarithm

\newline

7 \log a-x \log d

\newline

Answer:

\log (\square)

Rewrite using power rule: We are given the expression $7\log(a) - x\log(d)$ and we need to condense it into a single logarithm. $\newline$ According to the properties of logarithms, specifically the power rule which states that $n\log_b(m) = \log_b(m^n)$ , we can rewrite each term as follows: $\newline$ $7\log(a)$ becomes $\log(a^7)$ and $x\log(d)$ becomes $\log(d^x)$ .
Combine using quotient rule: Now we have $\log(a^7) - \log(d^x)$ . According to the quotient rule of logarithms, which states that $\log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right)$ , we can combine these two logarithms into a single logarithm with a quotient inside. $\newline$ So, $\log(a^7) - \log(d^x)$ becomes $\log\left(\frac{a^7}{d^x}\right)$ .
Final condensed expression: We have successfully condensed the original expression into a single logarithm. The final answer is $\log\left(\frac{a^7}{d^x}\right)$ .

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