Write the expression below as a single logarithm in simplest form. log_(b)6-log_(b)2 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the logarithms. We have the expression log_b(6) - log_b(2), which involves the subtraction of two logarithms with the same base b. The property that allows us to combine these logarithms is the quotient property of logarithms. Quotient Property: log_b(P) - log_b(Q) = log_b(P/Q)Apply Quotient Property: Apply the quotient property to combine the logarithms. Using the quotient property, we can write the expression as a single logarithm: log_b(6) - log_b(2) = log_b(6/2)Simplify Fraction: Simplify the fraction inside the logarithm. Simplify the fraction 6/2 to get 3: log_b(6/2) = log_b(3)Write Final Answer: Write the final answer. The expression log_b(6) - log_b(2) as a single logarithm in simplest form is log_b(3).

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

log_(b)6-log_(b)2
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 6-\log _{b} 2$ $\newline$ Answer: $\log _{b}(\square)$

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Algebra 2

Quotient property of logarithms

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

\newline

\log _{b} 6-\log _{b} 2

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the logarithms. $\newline$ We have the expression $\log_b(6) - \log_b(2)$ , which involves the subtraction of two logarithms with the same base $b$ . $\newline$ The property that allows us to combine these logarithms is the quotient property of logarithms. $\newline$ Quotient Property: $\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)$
Apply Quotient Property: Apply the quotient property to combine the logarithms. $\newline$ Using the quotient property, we can write the expression as a single logarithm: $\newline$ $\log_b(6) - \log_b(2) = \log_b\left(\frac{6}{2}\right)$
Simplify Fraction: Simplify the fraction inside the logarithm. $\newline$ Simplify the fraction $\frac{6}{2}$ to get $3$ : $\newline$ $\log_b\left(\frac{6}{2}\right) = \log_b(3)$
Write Final Answer: Write the final answer. $\newline$ The expression $\log_b(6) - \log_b(2)$ as a single logarithm in simplest form is $\log_b(3)$ .