Write the expression below as a single logarithm in simplest form. log_(b)6+log_(b)7 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the sum of logarithms. The sum of two logarithms with the same base can be combined using the product property of logarithms. Product Property: log_b (P) + log_b (Q) = log_b (P * Q)Apply Product Property: Apply the product property to combine log_(b)6 and log_(b)7. Using the product property, we can write the sum of log_(b)6 and log_(b)7 as a single logarithm of the product of 6 and 7. log_(b)6 + log_(b)7 = log_(b)(6 * 7)Calculate Product: Calculate the product of 6 and 7. To find the value inside the logarithm, we multiply 6 by 7. 6 * 7 = 42Write Final Expression: Write the final expression as a single logarithm. Now that we have the product, we can write the final expression as: log_(b)(42)

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

log_(b)6+log_(b)7
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 6+\log _{b} 7$ $\newline$ 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} 7

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the sum of logarithms. $\newline$ The sum of two logarithms with the same base can be combined using the product property of logarithms. $\newline$ Product Property: $\log_b (P) + \log_b (Q) = \log_b (P \times Q)$
Apply Product Property: Apply the product property to combine $\log_{b}6$ and $\log_{b}7$ . Using the product property, we can write the sum of $\log_{b}6$ and $\log_{b}7$ as a single logarithm of the product of $6$ and $7$ . $\newline$ $\log_{b}6 + \log_{b}7 = \log_{b}(6 \times 7)$
Calculate Product: Calculate the product of $6$ and $7$ . $\newline$ To find the value inside the logarithm, we multiply $6$ by $7$ . $\newline$ $6 \times 7 = 42$
Write Final Expression: Write the final expression as a single logarithm. $\newline$ Now that we have the product, we can write the final expression as: $\newline$ $\log_{b}(42)$