Find the numerical value of the log expression. {:[log a=-12quad log b=-8quad log c=-6],[log ((sqrt(b^(3)c^(3)))/(a^(9)))]:} Answer:

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Find the numerical value of the log expression.  {:[log a=-12quad log b=-8quad log c=-6],[log ((sqrt(b^(3)c^(3)))/(a^(9)))]:} Answer:

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Given values: We are given the values of $ \log a $, $ \log b $, and $ \log c $ as -12, -8, and -6 respectively. We need to find the value of $ \log \left( \frac{\sqrt{b^3 c^3}}{a^9} \right) $.Simplify expression: First, let's simplify the expression inside the logarithm. The square root of a product can be written as the product of the square roots, and the square root of a power can be written as the power with half the exponent. So, $ \sqrt{b^3 c^3} = \sqrt{b^3} \cdot \sqrt{c^3} = b^{3/2} \cdot c^{3/2} $.Rewrite using properties: Now, we can rewrite the logarithm using the properties of logarithms. The logarithm of a quotient is the difference of the logarithms, and the logarithm of a product is the sum of the logarithms. So, $ \log \left( \frac{\sqrt{b^3 c^3}}{a^9} \right) = \log(b^{3/2} \cdot c^{3/2}) - \log(a^9) $.Apply power rule: Applying the power rule for logarithms, which states that $ \log(x^y) = y \cdot \log(x) $, we get $ \log(b^{3/2} \cdot c^{3/2}) - \log(a^9) = \frac{3}{2} \cdot \log(b) + \frac{3}{2} \cdot \log(c) - 9 \cdot \log(a) $.Substitute values: Substituting the given values of $ \log a $, $ \log b $, and $ \log c $ into the expression, we get $ \frac{3}{2} \cdot (-8) + \frac{3}{2} \cdot (-6) - 9 \cdot (-12) $.Perform calculations: Performing the calculations, we have $ \frac{3}{2} \cdot (-8) = -12 $, $ \frac{3}{2} \cdot (-6) = -9 $, and $ 9 \cdot (-12) = -108 $. So, the expression simplifies to $ -12 + (-9) - (-108) $.Final numerical value: Finally, we add the numbers together to get the numerical value of the log expression: $ -12 - 9 + 108 = 87 $.

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=-12 \quad \log b=-8 \quad \log c=-6 \\ \log \frac{\sqrt{b^{3} c^{3}}}{a^{9}} \end{array}$ $\newline$ Answer:

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Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=-12 \quad \log b=-8 \quad \log c=-6 \\ \log \frac{\sqrt{b^{3} c^{3}}}{a^{9}} \end{array}$ $\newline$ Answer: