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

Identify Property Used: Identify the property used to combine the logarithms. The expression log_b(2) + 2log_b(2) involves a sum of logarithms and a multiplication by a constant within a logarithm. The Power Property of logarithms states that n*log_b(x) = log_b(x^n), and the Product Property states that log_b(x) + log_b(y) = log_b(xy).Apply Power Property: Apply the Power Property to the term 2log_b(2). Using the Power Property, we can rewrite 2log_b(2) as log_b(2^2). log_b(2^2) = log_b(4)Combine Using Product Property: Combine the logarithms using the Product Property. Now we have log_b(2) + log_b(4), which can be combined using the Product Property. log_b(2) + log_b(4) = log_b(2*4)Simplify Inside Logarithm: Simplify the expression inside the logarithm. Multiplying the numbers inside the logarithm gives us: log_b(2*4) = log_b(8)

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

log_(b)2+2log_(b)2
Answer:
log_(b)(◻)

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

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

\newline

Answer:

\log _{b}(\square)

Identify Property Used: Identify the property used to combine the logarithms. $\newline$ The expression $\log_b(2) + 2\log_b(2)$ involves a sum of logarithms and a multiplication by a constant within a logarithm. $\newline$ The Power Property of logarithms states that $n\log_b(x) = \log_b(x^n)$ , and the Product Property states that $\log_b(x) + \log_b(y) = \log_b(xy)$ .
Apply Power Property: Apply the Power Property to the term $2\log_b(2)$ . Using the Power Property, we can rewrite $2\log_b(2)$ as $\log_b(2^2)$ . $\log_b(2^2) = \log_b(4)$
Combine Using Product Property: Combine the logarithms using the Product Property. $\newline$ Now we have $\log_b(2) + \log_b(4)$ , which can be combined using the Product Property. $\newline$ $\log_b(2) + \log_b(4) = \log_b(2\times4)$
Simplify Inside Logarithm: Simplify the expression inside the logarithm. $\newline$ Multiplying the numbers inside the logarithm gives us: $\newline$ $\log_b(2\times4) = \log_b(8)$