Write the expression below as a single logarithm in simplest form. log_(b)5+log_(b)4 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the logarithms. The expression log_b(5) + log_b(4) involves the sum of two logarithms with the same base b. The Product Property of logarithms states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments. Product Property: log_b(P) + log_b(Q) = log_b(P * Q)Apply Property: Apply the Product Property to combine log_b(5) and log_b(4). Using the Product Property, we can combine the two logarithms into a single logarithm by multiplying their arguments. log_b(5) + log_b(4) = log_b(5 * 4)Perform Multiplication: Perform the multiplication inside the logarithm. Now we multiply the numbers inside the logarithm to simplify the expression. 5 * 4 = 20 So, log_b(5) + log_b(4) = log_b(20)

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

log_(b)5+log_(b)4
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 5+\log _{b} 4$ $\newline$ 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} 5+\log _{b} 4

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the logarithms. $\newline$ The expression $\log_b(5) + \log_b(4)$ involves the sum of two logarithms with the same base $b$ . $\newline$ The Product Property of logarithms states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments. $\newline$ Product Property: $\log_b(P) + \log_b(Q) = \log_b(P \times Q)$
Apply Property: Apply the Product Property to combine $\log_b(5)$ and $\log_b(4)$ . Using the Product Property, we can combine the two logarithms into a single logarithm by multiplying their arguments. $\log_b(5) + \log_b(4) = \log_b(5 \times 4)$
Perform Multiplication: Perform the multiplication inside the logarithm. $\newline$ Now we multiply the numbers inside the logarithm to simplify the expression. $\newline$ $5 \times 4 = 20$ $\newline$ So, $\log_b(5) + \log_b(4) = \log_b(20)$