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

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

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Identify Given Values: Identify the given logarithmic values and the expression to be evaluated. We are given: log a = 4 log b = -8 log c = -3 We need to find the value of log ((sqrt(a^(3)b^(5)))/(c^(5))).Apply Logarithmic Properties: Apply the properties of logarithms to the expression. Using the quotient rule of logarithms, which states that log(x/y) = log(x) - log(y), we can write: log ((sqrt(a^(3)b^(5)))/(c^(5))) = log (sqrt(a^(3)b^(5))) - log (c^(5))Apply Power Rule: Apply the power rule of logarithms to the expression inside the square root. The power rule states that log(x^k) = k * log(x). Since we have a square root, which is equivalent to the power of 1/2, we can write: log (sqrt(a^(3)b^(5))) = (1/2) * log (a^(3)b^(5))Apply Product Rule: Apply the product rule of logarithms to the expression inside the logarithm. The product rule states that log(xy) = log(x) + log(y). Therefore: (1/2) * log (a^(3)b^(5)) = (1/2) * (log (a^(3)) + log (b^(5)))Apply Power Rule: Apply the power rule to the individual logarithms. log (a^(3)) = 3 * log (a) log (b^(5)) = 5 * log (b) So, (1/2) * (log (a^(3)) + log (b^(5))) = (1/2) * (3 * log (a) + 5 * log (b))Substitute Given Values: Substitute the given values of log a and log b into the expression. log a = 4 and log b = -8, so: (1/2) * (3 * log (a) + 5 * log (b)) = (1/2) * (3 * 4 + 5 * (-8))Perform Arithmetic Operations: Perform the arithmetic operations. (1/2) * (3 * 4 + 5 * (-8)) = (1/2) * (12 - 40) = (1/2) * (-28) = -14Apply Power Rule: Apply the power rule to the logarithm of c^(5). log (c^(5)) = 5 * log (c) Substitute the given value of log c: 5 * log (c) = 5 * (-3)Perform Arithmetic Operation: Perform the arithmetic operation for log (c^(5)). 5 * (-3) = -15Combine Results: Combine the results from Step 7 and Step 9 using the result from Step 2. log ((sqrt(a^(3)b^(5)))/(c^(5))) = -14 - (-15)Perform Final Arithmetic: Perform the final arithmetic operation to find the numerical value. -14 - (-15) = -14 + 15 = 1

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

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