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

2log_(b)3
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $2 \log _{b} 3$ $\newline$ 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

2 \log _{b} 3

\newline

Answer:

\log _{b}(\square)

Question Prompt: Question Prompt: Write the expression $2\log_{b}3$ as a single logarithm in simplest form.
Identify Property: Identify the property used to write the expression as a single logarithm. $\newline$ The expression $2\log_{b}3$ involves a logarithm with a coefficient. To write this as a single logarithm, we use the power property of logarithms. $\newline$ Power Property: $a\log_{b}(P) = \log_{b}(P^{a})$
Apply Property: Apply the power property to the given expression. $\newline$ Using the power property, we can move the coefficient $2$ inside the logarithm as an exponent of the argument. $\newline$ $2\log_{b}3 = \log_{b}(3^2)$
Calculate Exponent: Calculate the exponent. $\newline$ $3^2 = 9$ $\newline$ So, $\log_{b}(3^2)$ becomes $\log_{b}(9)$ .
Write Final Answer: Write the final answer. $\newline$ The expression $2\log_{b}3$ written as a single logarithm in simplest form is $\log_{b}(9)$ .

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