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

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

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Apply Logarithm Power Rule: Apply the logarithm power rule to the expression. The power rule of logarithms states that log(a^n) = n * log(a). Let's apply this rule to each term in the expression. log(a^(9)) = 9 * log(a) log(b^(9)) = 9 * log(b) log(c^(8)) = 8 * log(c)Substitute Given Log Values: Substitute the given logarithm values into the expression. We have been given log a = -8, log b = 9, and log c = -3. Let's substitute these values into the expression from Step 1. log(a^(9)) = 9 * (-8) log(b^(9)) = 9 * 9 log(c^(8)) = 8 * (-3)Calculate Values: Calculate the values from Step 2. Now we calculate the numerical values for each term. log(a^(9)) = 9 * (-8) = -72 log(b^(9)) = 9 * 9 = 81 log(c^(8)) = 8 * (-3) = -24Apply Logarithm Quotient Rule: Apply the logarithm quotient rule to the original expression. The quotient rule of logarithms states that log(a/b) = log(a) - log(b). Let's apply this rule to the original expression. log((a^(9)b^(9))/(c^(8))) = log(a^(9)) + log(b^(9)) - log(c^(8))Substitute Calculated Values: Substitute the calculated values from Step 3 into the expression from Step 4. Now we substitute the values we found into the expression. log((a^(9)b^(9))/(c^(8))) = (-72) + 81 - (-24)Calculate Final Value: Calculate the final numerical value. Now we perform the arithmetic to find the numerical value. log((a^(9)b^(9))/(c^(8))) = (-72) + 81 + 24 log((a^(9)b^(9))/(c^(8))) = 9 + 24 log((a^(9)b^(9))/(c^(8))) = 33

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

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