Write the expression below as a single logarithm in simplest form. 4log_(b)2+log_(b)5 Answer: log_(b)(◻)

Identify Properties: Identify the properties used to combine the logarithms. The expression contains two logarithms that are being added together. To combine them into a single logarithm, we can use the product property of logarithms. Product Property: log_b (M) + log_b (N) = log_b (M * N) However, before we can apply the product property directly, we need to address the coefficient 4 in front of the first logarithm. This can be done using the power property of logarithms. Power Property: k * log_b (M) = log_b (M^k)Apply Power Property: Apply the power property to the term with the coefficient. We have 4log_(b)2, which can be rewritten using the power property as log_(b)(2^4). Calculation: 2^4 = 16 So, 4log_(b)2 becomes log_(b)16.Combine Logarithms: Combine the two logarithms using the product property. Now we have log_(b)16 + log_(b)5, which can be combined into a single logarithm using the product property. Calculation: log_(b)(16 * 5) Since 16 * 5 = 80, we get log_(b)80.

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

4log_(b)2+log_(b)5
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $4 \log _{b} 2+\log _{b} 5$ $\newline$ Answer: $\log _{b}(\square)$

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Math Problems

Algebra 2

Quotient property of logarithms

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

\newline

4 \log _{b} 2+\log _{b} 5

\newline

Answer:

\log _{b}(\square)

Identify Properties: Identify the properties used to combine the logarithms. $\newline$ The expression contains two logarithms that are being added together. To combine them into a single logarithm, we can use the product property of logarithms. $\newline$ Product Property: $\log_b (M) + \log_b (N) = \log_b (M \times N)$ $\newline$ However, before we can apply the product property directly, we need to address the coefficient $4$ in front of the first logarithm. This can be done using the power property of logarithms. $\newline$ Power Property: $k \times \log_b (M) = \log_b (M^k)$
Apply Power Property: Apply the power property to the term with the coefficient. $\newline$ We have $4\log_{b}2$ , which can be rewritten using the power property as $\log_{b}(2^4)$ . $\newline$ Calculation: $2^4 = 16$ $\newline$ So, $4\log_{b}2$ becomes $\log_{b}16$ .
Combine Logarithms: Combine the two logarithms using the product property. $\newline$ Now we have $\log_{b}16 + \log_{b}5$ , which can be combined into a single logarithm using the product property. $\newline$ Calculation: $\log_{b}(16 \times 5)$ $\newline$ Since $16 \times 5 = 80$ , we get $\log_{b}80$ .