Write the expression below as a single logarithm in simplest form. 3log_(b)3-log_(b)3 Answer: log_(b)(◻)

Identify Properties: Identify the properties of logarithms that can be applied. We have the expression 3log_(b)3 - log_(b)3. We can use the power rule of logarithms to rewrite the first term, which states that n*log_b(a) = log_b(a^n).Apply Power Rule: Apply the power rule to the first term. Using the power rule, we can rewrite 3log_(b)3 as log_(b)(3^3).Simplify Exponent: Simplify the exponent. Calculate 3^3 to simplify the expression. 3^3 = 27 So, log_(b)(3^3) becomes log_(b)(27).Combine Logarithms: Combine the logarithms. Now we have log_(b)(27) - log_(b)3. We can use the quotient rule of logarithms, which states that log_b(a) - log_b(c) = log_b(a/c), to combine these into a single logarithm.Apply Quotient Rule: Apply the quotient rule. Using the quotient rule, we combine log_(b)(27) and log_(b)3 into log_(b)(27/3).Simplify Fraction: Simplify the fraction inside the logarithm. Calculate 27/3 to simplify the expression inside the logarithm. 27/3 = 9 So, log_(b)(27/3) becomes log_(b)(9).

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Write the expression below as a single logarithm in simplest form.

3log_(b)3-log_(b)3
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $3 \log _{b} 3-\log _{b} 3$ $\newline$ Answer: $\log _{b}(\square)$

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Precalculus

Quotient property of logarithms

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Q. Write the expression below as a single logarithm in simplest form.

\newline

3 \log _{b} 3-\log _{b} 3

\newline

Answer:

\log _{b}(\square)

Identify Properties: Identify the properties of logarithms that can be applied. $\newline$ We have the expression $3\log_{b}3 - \log_{b}3$ . We can use the power rule of logarithms to rewrite the first term, which states that $n\log_b(a) = \log_b(a^n)$ .
Apply Power Rule: Apply the power rule to the first term. $\newline$ Using the power rule, we can rewrite $3\log_{b}3$ as $\log_{b}(3^3)$ .
Simplify Exponent: Simplify the exponent. $\newline$ Calculate $3^3$ to simplify the expression. $\newline$ $3^3 = 27$ $\newline$ So, $\log_{b}(3^3)$ becomes $\log_{b}(27)$ .
Combine Logarithms: Combine the logarithms. $\newline$ Now we have $\log_{b}(27) - \log_{b}3$ . We can use the quotient rule of logarithms, which states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ , to combine these into a single logarithm.
Apply Quotient Rule: Apply the quotient rule. Using the quotient rule, we combine $\log_{b}(27)$ and $\log_{b}3$ into $\log_{b}\left(\frac{27}{3}\right)$ .
Simplify Fraction: Simplify the fraction inside the logarithm. $\newline$ Calculate $\frac{27}{3}$ to simplify the expression inside the logarithm. $\newline$ $\frac{27}{3} = 9$ $\newline$ So, $\log_{b}\left(\frac{27}{3}\right)$ becomes $\log_{b}(9)$ .