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

Recognize Properties: Recognize the properties of logarithms that can be applied. The expression given is a combination of two logarithms with the same base that are being subtracted. We can use the power property of logarithms to rewrite the first term and the quotient property to combine the terms into a single logarithm.Apply Power Property: Apply the power property to the first term. The power property of logarithms states that log_b(a^n) = n * log_b(a). We can apply this property to the first term to rewrite 5log_(b)2 as log_(b)(2^5). Calculation: 2^5 = 32Combine Using Quotient Property: Combine the two logarithms using the quotient property. The quotient property of logarithms states that log_b(a) - log_b(c) = log_b(a/c). We can apply this property to combine log_(b)(32) and log_(b)4 into a single logarithm. Calculation: log_(b)(32/4)Simplify Inside Logarithm: Simplify the expression inside the logarithm. We need to divide 32 by 4 to simplify the expression inside the logarithm. Calculation: 32 / 4 = 8Write Final Answer: Write the final answer. The expression 5log_(b)2 - log_(b)4 can be written as a single logarithm as log_(b)(8).

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

5log_(b)2-log_(b)4
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $5 \log _{b} 2-\log _{b} 4$ $\newline$ 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

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

\newline

Answer:

\log _{b}(\square)

Recognize Properties: Recognize the properties of logarithms that can be applied. $\newline$ The expression given is a combination of two logarithms with the same base that are being subtracted. We can use the power property of logarithms to rewrite the first term and the quotient property to combine the terms into a single logarithm.
Apply Power Property: Apply the power property to the first term. $\newline$ The power property of logarithms states that $\log_b(a^n) = n \cdot \log_b(a)$ . We can apply this property to the first term to rewrite $5\log_{b}2$ as $\log_{b}(2^5)$ . $\newline$ Calculation: $2^5 = 32$
Combine Using Quotient Property: Combine the two logarithms using the quotient property. $\newline$ The quotient property of logarithms states that $\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)$ . We can apply this property to combine $\log_{b}(32)$ and $\log_{b}(4)$ into a single logarithm. $\newline$ Calculation: $\log_{b}\left(\frac{32}{4}\right)$
Simplify Inside Logarithm: Simplify the expression inside the logarithm. $\newline$ We need to divide $32$ by $4$ to simplify the expression inside the logarithm. $\newline$ Calculation: $32 / 4 = 8$
Write Final Answer: Write the final answer. $\newline$ The expression $5\log_{b}2 - \log_{b}4$ can be written as a single logarithm as $\log_{b}(8)$ .