Write the expression below as a single logarithm in simplest form. 2log_(b)3+log_(b)6 Answer: log_(b)(◻)

Identify Properties: Identify the properties used to combine logarithms. The expression 2log_(b)3 + log_(b)6 involves two logarithmic terms that can be combined using the power property and the product property of logarithms. Power Property: log_b (P^k) = k * log_b P Product Property: log_b P + log_b Q = log_b (P * Q)Apply Power Property: Apply the power property to the first term. The power property allows us to move the coefficient of the logarithm inside as an exponent of the argument. 2log_(b)3 = log_(b)(3^2)Simplify Exponent: Simplify the exponent. Calculate the value of 3^2. 3^2 = 9 So, 2log_(b)3 becomes log_(b)9.Apply Product Property: Apply the product property to combine the logarithms. Now, we can use the product property to combine log_(b)9 and log_(b)6 into a single logarithm. log_(b)9 + log_(b)6 = log_(b)(9 * 6)Calculate Product: Calculate the product inside the logarithm. Multiply 9 by 6 to get the argument of the combined logarithm. 9 * 6 = 54 So, log_(b)9 + log_(b)6 becomes log_(b)54.Write Final Answer: Write the final answer. The expression 2log_(b)3 + log_(b)6 as a single logarithm in simplest form is: log_(b)54

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

2log_(b)3+log_(b)6
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $2 \log _{b} 3+\log _{b} 6$ $\newline$ 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

2 \log _{b} 3+\log _{b} 6

\newline

Answer:

\log _{b}(\square)

Identify Properties: Identify the properties used to combine logarithms. $\newline$ The expression $2\log_{b}3 + \log_{b}6$ involves two logarithmic terms that can be combined using the power property and the product property of logarithms. $\newline$ Power Property: $\log_b (P^k) = k \cdot \log_b P$ $\newline$ Product Property: $\log_b P + \log_b Q = \log_b (P \cdot Q)$
Apply Power Property: Apply the power property to the first term. $\newline$ The power property allows us to move the coefficient of the logarithm inside as an exponent of the argument. $\newline$ $2\log_{b}3 = \log_{b}(3^2)$
Simplify Exponent: Simplify the exponent. $\newline$ Calculate the value of $3^2$ . $\newline$ $3^2 = 9$ $\newline$ So, $2\log_{b}3$ becomes $\log_{b}9$ .
Apply Product Property: Apply the product property to combine the logarithms. $\newline$ Now, we can use the product property to combine $\log_{b}9$ and $\log_{b}6$ into a single logarithm. $\newline$ $\log_{b}9 + \log_{b}6 = \log_{b}(9 \times 6)$
Calculate Product: Calculate the product inside the logarithm. $\newline$ Multiply $9$ by $6$ to get the argument of the combined logarithm. $\newline$ $9 \times 6 = 54$ $\newline$ So, $\log_{b}9 + \log_{b}6$ becomes $\log_{b}54$ .
Write Final Answer: Write the final answer. $\newline$ The expression $2\log_{b}3 + \log_{b}6$ as a single logarithm in simplest form is: $\newline$ $\log_{b}54$