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

5log_(b)2
Answer:
log_(b)(◻)

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

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Quotient property of logarithms

Full solution

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

\newline

5 \log _{b} 2

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to rewrite the expression $5\log_{b}2$ as a single logarithm. $\newline$ The Power Property of logarithms states that a coefficient can be rewritten as an exponent inside the logarithm. $\newline$ Power Property: $a \cdot \log_b (P) = \log_b (P^a)$
Apply Power Property: Apply the Power Property to rewrite $5\log_{b}2$ as a single logarithm. $\newline$ Using the Power Property, we can move the coefficient $5$ inside the logarithm as an exponent of $2$ . $\newline$ So, $5\log_{b}2$ becomes $\log_{b}(2^5)$ .
Calculate Value: Calculate the value of $2^5$ to simplify the expression further. $\newline$ $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$
Write Final Expression: Write the final expression as a single logarithm. $\newline$ The expression $5\log_{b}2$ is now written as $\log_{b}(32)$ .

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