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Write the expression
2ln 2-ln 3 as a single logarithm in simplest form without any negative exponents.
Answer:
ln(◻)

Write the expression $2 \ln 2-\ln 3$ as a single logarithm in simplest form without any negative exponents. $\newline$ Answer: $\ln (\square)$

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Change of base formula

Full solution

Q. Write the expression

2 \ln 2-\ln 3

as a single logarithm in simplest form without any negative exponents.

\newline

Answer:

\ln (\square)

Apply power rule: Apply the power rule of logarithms to the term $2\ln 2$ . The power rule states that $a \cdot \log_b(c) = \log_b(c^a)$ . Therefore, $2\ln 2$ can be rewritten as $\ln(2^2)$ . Calculation: $\ln(2^2) = \ln(4)$
Rewrite term as $\ln(4)$ : Combine the two logarithmic terms using the quotient rule. $\newline$ The quotient rule states that $\log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right)$ . $\newline$ Therefore, $\ln(4) - \ln(3)$ can be combined into a single logarithm. $\newline$ Calculation: $\ln(4) - \ln(3) = \ln\left(\frac{4}{3}\right)$

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