Write the expression below as a single logarithm in simplest form. log_(b)3+log_(b)2 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine log_b(3) and log_b(2). When adding two logarithms with the same base, we can use the product property of logarithms. Product Property: log_b (M) + log_b (N) = log_b (M * N)Apply Property: Apply the product property to combine log_b(3) and log_b(2). Using the product property, we combine the two logarithms: log_b(3) + log_b(2) = log_b(3 * 2)Perform Multiplication: Perform the multiplication inside the logarithm. Multiply the constants inside the logarithm: log_b(3 * 2) = log_b(6)Check Simplified Form: Check if the expression is in the simplest form. The expression log_b(6) is already in the simplest form because it is a single logarithm with a distinct constant inside.

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

log_(b)3+log_(b)2
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 3+\log _{b} 2$ $\newline$ Answer: $\log _{b}(\square)$

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Algebra 2

Quotient property of logarithms

Full solution

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

\newline

\log _{b} 3+\log _{b} 2

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine $\log_b(3)$ and $\log_b(2)$ . When adding two logarithms with the same base, we can use the product property of logarithms. $\newline$ Product Property: $\log_b (M) + \log_b (N) = \log_b (M \times N)$
Apply Property: Apply the product property to combine $\log_b(3)$ and $\log_b(2)$ . $\newline$ Using the product property, we combine the two logarithms: $\newline$ $\log_b(3) + \log_b(2) = \log_b(3 \times 2)$
Perform Multiplication: Perform the multiplication inside the logarithm. $\newline$ Multiply the constants inside the logarithm: $\newline$ $\log_b(3 \times 2) = \log_b(6)$
Check Simplified Form: Check if the expression is in the simplest form. $\newline$ The expression $\log_b(6)$ is already in the simplest form because it is a single logarithm with a distinct constant inside.