Identify Properties: Identify the properties of logarithms that can be used to combine the logarithms. We can use the product rule of logarithms to combine log_9(5) and log_9(8) into a single logarithm. The product rule states that log_b(m) + log_b(n) = log_b(m*n), where b is the base of the logarithms.Apply Product Rule: Apply the product rule to combine the logarithms. Using the product rule, we can write log_9(5) + log_9(8) as log_9(5*8).Perform Multiplication: Perform the multiplication inside the logarithm. Now we calculate the product inside the logarithm: 5*8 = 40. So, log_9(5) + log_9(8) becomes log_9(40).Check for Simplification: Check if the logarithm can be simplified further. Since 40 is not a power of 9, and there are no obvious factors of 40 that are powers of 9, we cannot simplify the logarithm further. Therefore, log_9(40) is the final answer.

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$\log_{9}5+\log_{9}8=$

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Precalculus

Quotient property of logarithms

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\log_{9}5+\log_{9}8=

Identify Properties: Identify the properties of logarithms that can be used to combine the logarithms. $\newline$ We can use the product rule of logarithms to combine $\log_9(5)$ and $\log_9(8)$ into a single logarithm. The product rule states that $\log_b(m) + \log_b(n) = \log_b(m*n)$ , where $b$ is the base of the logarithms.
Apply Product Rule: Apply the product rule to combine the logarithms. $\newline$ Using the product rule, we can write $\log_9(5) + \log_9(8)$ as $\log_9(5*8)$ .
Perform Multiplication: Perform the multiplication inside the logarithm. $\newline$ Now we calculate the product inside the logarithm: $5 \times 8 = 40$ . $\newline$ So, $\log_9(5) + \log_9(8)$ becomes $\log_9(40)$ .
Check for Simplification: Check if the logarithm can be simplified further. $\newline$ Since $40$ is not a power of $9$ , and there are no obvious factors of $40$ that are powers of $9$ , we cannot simplify the logarithm further. Therefore, $ext{log}_9(40)$ is the final answer.