Find the numerical value of the log expression. {:[log a=-3quad log b=-11quad log c=8],[log ((root(3)(a))/(b^(4)c^(5)))]:} Answer:

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Find the numerical value of the log expression.  {:[log a=-3quad log b=-11quad log c=8],[log ((root(3)(a))/(b^(4)c^(5)))]:} Answer:

Bytelearn · Accepted Answer

Apply Properties of Logarithms: Let's start by applying the properties of logarithms to the expression $ \log \left( \frac{\sqrt[3]{a}}{b^4 c^5} \right) $. We can use the quotient rule of logarithms, which states that $ \log \left( \frac{x}{y} \right) = \log(x) - \log(y) $, and the power rule, which states that $ \log(x^k) = k \cdot \log(x) $.Apply Quotient Rule: First, apply the quotient rule to the given expression: $ \log \left( \frac{\sqrt[3]{a}}{b^4 c^5} \right) = \log(\sqrt[3]{a}) - \log(b^4 c^5) $.Apply Power Rule: Next, apply the power rule to the terms $ \log(b^4) $ and $ \log(c^5) $: $ \log(\sqrt[3]{a}) - \log(b^4 c^5) = \log(\sqrt[3]{a}) - (4 \cdot \log(b) + 5 \cdot \log(c)) $.Express as Power of a: Now, we need to express $ \log(\sqrt[3]{a}) $ as a power of $ a $: Since $ \sqrt[3]{a} = a^{1/3} $, we can write $ \log(\sqrt[3]{a}) $ as $ \frac{1}{3} \cdot \log(a) $.Substitute Given Values: Substitute the given values of $ \log(a) $, $ \log(b) $, and $ \log(c) $ into the expression: $ \frac{1}{3} \cdot \log(a) - (4 \cdot \log(b) + 5 \cdot \log(c)) = \frac{1}{3} \cdot (-3) - (4 \cdot (-11) + 5 \cdot 8) $.Perform Arithmetic Operations: Perform the arithmetic operations: $ \frac{1}{3} \cdot (-3) - (4 \cdot (-11) + 5 \cdot 8) = -1 - (-44 + 40) = -1 - (-4) = -1 + 4 = 3 $.

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=-3 \quad \log b=-11 \quad \log c=8 \\ \log \frac{\sqrt[3]{a}}{b^{4} c^{5}} \end{array}$ $\newline$ Answer:

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Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=-3 \quad \log b=-11 \quad \log c=8 \\ \log \frac{\sqrt[3]{a}}{b^{4} c^{5}} \end{array}$ $\newline$ Answer: