log_(9)((x^(3))/(16))

Apply Logarithm Property: We need to simplify the logarithmic expression log_(9)((x^(3))/(16)). The base of the logarithm is 9, and the argument is (x^(3))/(16).Simplify Logarithm of x^3: Recall the logarithm property that allows us to write the logarithm of a quotient as the difference of two logarithms: log_b(a/c) = log_b(a) - log_b(c). Apply this property to the given expression. log_(9)((x^(3))/(16)) = log_(9)(x^(3)) - log_(9)(16)Simplify Logarithm of 16: Now, we can simplify each term separately. Starting with log_(9)(x^(3)), we can use the power rule of logarithms, which states that log_b(a^c) = c * log_b(a), to simplify this term. log_(9)(x^(3)) = 3 * log_(9)(x)Combine Simplified Terms: Next, we simplify log_(9)(16). Since 16 is not an obvious power of 9, we cannot directly simplify this term further. So, it remains as log_(9)(16).Combine the simplified terms to get the final expression. log_(9)((x^(3))/(16)) = 3 * log_(9)(x) - log_(9)(16)

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\log_{9}\left(\frac{x^{3}}{16}\right)

Apply Logarithm Property: We need to simplify the logarithmic expression $\log_{9}\left(\frac{x^{3}}{16}\right)$ . The base of the logarithm is $9$ , and the argument is $\frac{x^{3}}{16}$ .
Simplify Logarithm of $x^3$ : Recall the logarithm property that allows us to write the logarithm of a quotient as the difference of two logarithms: $\log_b\left(\frac{a}{c}\right) = \log_b(a) - \log_b(c)$ . Apply this property to the given expression. $\newline$ $\log_{9}\left(\frac{x^{3}}{16}\right) = \log_{9}(x^{3}) - \log_{9}(16)$
Simplify Logarithm of $16$ : Now, we can simplify each term separately. Starting with $\log_{9}(x^{3})$ , we can use the power rule of logarithms, which states that $\log_{b}(a^{c}) = c \cdot \log_{b}(a)$ , to simplify this term. $\newline$ $\log_{9}(x^{3}) = 3 \cdot \log_{9}(x)$
Combine Simplified Terms: Next, we simplify $\log_{9}(16)$ . Since $16$ is not an obvious power of $9$ , we cannot directly simplify this term further. So, it remains as $\log_{9}(16)$ .
Combine Simplified Terms: Next, we simplify $\log_{9}(16)$ . Since $16$ is not an obvious power of $9$ , we cannot directly simplify this term further. So, it remains as $\log_{9}(16)$ .Combine the simplified terms to get the final expression. $\newline$ $\log_{9}\left(\frac{x^{3}}{16}\right) = 3 \cdot \log_{9}(x) - \log_{9}(16)$