Write the expression below as a single logarithm in simplest form. log_(b)10+log_(b)8 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the logarithms. The given expression is the sum of two logarithms with the same base b. The product property of logarithms states that the sum of two logarithms with the same base is the logarithm of the product of their arguments. Product Property: log_b (M) + log_b (N) = log_b (M * N)Apply Property: Apply the product property to combine log_(b)10 and log_(b)8. Using the product property, we can write: log_(b)10 + log_(b)8 = log_(b)(10 * 8)Calculate Product: Calculate the product inside the logarithm. Calculate the product of 10 and 8: 10 * 8 = 80Write Final Expression: Write the final expression as a single logarithm. The final expression is: log_(b)(80)

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

log_(b)10+log_(b)8
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 10+\log _{b} 8$ $\newline$ 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

\log _{b} 10+\log _{b} 8

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the logarithms. $\newline$ The given expression is the sum of two logarithms with the same base $b$ . $\newline$ The product property of logarithms states that the sum of two logarithms with the same base is the logarithm of the product of their arguments. $\newline$ Product Property: $\log_b (M) + \log_b (N) = \log_b (M \cdot N)$
Apply Property: Apply the product property to combine $\log_{b}10$ and $\log_{b}8$ . Using the product property, we can write: $\log_{b}10 + \log_{b}8 = \log_{b}(10 \times 8)$
Calculate Product: Calculate the product inside the logarithm. $\newline$ Calculate the product of $10$ and $8$ : $\newline$ $10 \times 8 = 80$
Write Final Expression: Write the final expression as a single logarithm. $\newline$ The final expression is: $\newline$ $\log_{b}(80)$