Find the numerical value of the log expression. {:[log a=1quad,log b=6quad log c=9],[log ((a^(4))/(root(3)(b^(7)c^(4))))]:} Answer:

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Find the numerical value of the log expression.  {:[log a=1quad,log b=6quad log c=9],[log ((a^(4))/(root(3)(b^(7)c^(4))))]:} Answer:

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Identify Given Values: Identify the given logarithmic values and the expression to be evaluated. We are given log a = 1, log b = 6, and log c = 9. We need to find the value of log ((a^(4))/(root(3)(b^(7)c^(4)))).Apply Power Rule: Apply the logarithm power rule to the numerator of the expression. The power rule of logarithms states that log(a^n) = n * log(a). Therefore, log(a^(4)) = 4 * log(a). Since log a = 1, we have log(a^(4)) = 4 * 1 = 4.Apply Power Rule to Denominator: Apply the logarithm power rule to the denominator of the expression. We have a cube root in the denominator, which can be written as a power of 1/3. The expression inside the cube root is b^(7)c^(4), which can be separated using the product rule of logarithms: log(b^(7)c^(4)) = log(b^(7)) + log(c^(4)). Now apply the power rule: log(b^(7)) = 7 * log(b) and log(c^(4)) = 4 * log(c). Since log b = 6 and log c = 9, we have log(b^(7)) = 7 * 6 = 42 and log(c^(4)) = 4 * 9 = 36.Combine Denominator Logarithms: Combine the logarithms of the denominator and apply the cube root. We have log(b^(7)) + log(c^(4)) = 42 + 36 = 78. Now, we need to apply the cube root, which is the same as multiplying by 1/3: (1/3) * log(b^(7)c^(4)) = (1/3) * 78 = 26.Use Quotient Rule: Use the quotient rule of logarithms to combine the numerator and denominator. The quotient rule of logarithms states that log(a/b) = log(a) - log(b). We have log(a^(4)) - log(root(3)(b^(7)c^(4))) = 4 - 26.Calculate Final Value: Calculate the final numerical value. Subtract the value found for the denominator from the numerator: 4 - 26 = -22.

Find the numerical value of the log expression. $\newline$ $\begin{array}{cc} \log a=1 \quad & \log b=6 \quad \log c=9 \\ \log \frac{a^{4}}{\sqrt[3]{b^{7} c^{4}}} \end{array}$ $\newline$ Answer:

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Find the numerical value of the log expression. $\newline$ $\begin{array}{cc} \log a=1 \quad & \log b=6 \quad \log c=9 \\ \log \frac{a^{4}}{\sqrt[3]{b^{7} c^{4}}} \end{array}$ $\newline$ Answer: